In computational flow analysis with moving solid surfaces and contact between the solid surfaces, it is a challenge to represent the boundary layers with an accuracy attributed to moving-mesh methods and to represent the contact without leaving a mesh protection gap. The space-time topology change (ST-TC) method, introduced in 2013, makes moving-mesh computation possible even when we have contact between moving solid surfaces or other kinds of flow-domain TC. The contact is represented without giving up on high-resolution flow representation near the moving surfaces. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting this class of flow analysis in the presence of additional complexities such as geometric complexity, rotation or deformation of the solid surfaces and the multiscale nature of the flow. In this first part of a two-part article, we provide an overview of the methods that made all that possible. We also provide an overview of the computations performed for tire aerodynamics with challenges that include the complexity of a near-actual tire geometry with grooves, road contact, tire deformation and rotation, road roughness and fluid films.

In computation of flow problems with moving boundaries and interfaces, including fluid-structure interaction, moving the fluid mechanics mesh to follow the fluid-solid interface enables mesh-resolution control near the interface. Therefore moving-mesh methods, such as the Space-Time Variational Multiscale (ST-VMS) method, enable high-resolution boundary-layer representation near fluid-solid interfaces and thus higher accuracy in such critical flow regions. In flow problems with contact between solid surfaces, until recently, one had to either give up on representing the actual contact and leave a small gap or give up on using a moving-mesh method and thus give up on having high-fidelity flow solution near the solid surfaces. The ST Topology Change (ST-TC) method changed all that. Now we can both represent the actual contact and have high-fidelity flow solution near the solid surfaces. With the ST-VMS, which serves as the core method, and the ST-TC and two other special methods, the ST Slip Interface method and ST Isogeometric Analysis, we have created a powerful computational framework. The new framework is enabling high-fidelity computational flow analysis of some of the most complex problems, such as the ventricle-valve-aorta sequence. This chapter is a description and demonstration of that framework.

The U-duct turbulent flow is a known benchmark problem with the computational challenges of high Reynolds number, high curvature and strong flow dependence on the inflow profile. We use this benchmark problem to test and evaluate the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization. A fully-developed flow field in a straight duct with periodicity condition is used as the inflow profile. The ST-VMS serves as the core method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The ST isogeometric discretization enables more accurate representation of the duct geometry and increased accuracy in the flow solution. In the straight-duct computations to obtain the inflow velocity, the periodicity condition is enforced with the ST Slip Interface method. All computations are carried out with quadratic NURBS meshes, which represent the circular arc of the duct exactly in the U-duct computations. We investigate how the results vary with the time-averaging range used in reporting the results, mesh refinement, and the Courant number. The results are compared to experimental data, showing that the ST-VMS with ST isogeometric discretization provides good accuracy in this class of flow problems.

Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels tn and tn+1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at tn. While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

The Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry accurately and provide a high-fidelity flow solution. We use the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization to address these computational challenges and to evaluate how the method and discretization perform under different scenarios of computing the Taylor–Couette flow. We conduct the computational analysis with different combinations of the Reynolds numbers based on the inner and outer cylinder rotation speeds, with different choices of the reference frame, one of which leads to rotating the mesh, with the full-domain and rotational-periodicity representations of the flow field, with both the convective and conservative forms of the ST-VMS, with both the strong and weak enforcement of the prescribed velocities on the cylinder surfaces, and with different mesh refinements. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables exact representation of the circular geometry and increased accuracy in the flow solution. In computations where the mesh is rotating, the ST/NURBS Mesh Update Method, with NURBS basis functions in time, enables exact representation of the mesh rotation, in terms of both the paths of the mesh points and the velocity of the points along their paths. In computations with rotational-periodicity representation of the flow field, the periodicity is enforced with the ST Slip Interface method. With the combinations of the Reynolds numbers used in the computations, we cover the cases leading to the Taylor vortex flow and the wavy vortex flow, where the waves are in motion. Our work shows that all these ST methods, integrated together, offer a high-fidelity computational analysis platform for the Taylor–Couette flow and for other classes of flow problems with similar features.

An earlier version of this article included a number of typesetting mistakes. These were corrected on October 16, 2020. The publisher apologizes for the errors made during production. The symbol “Λn” was incorrectly published as “Γn” in equations 46 and 47. The correct equations are provided in this correction.

A recently introduced NURBS mesh generation method for complex-geometry Isogeometric Analysis (IGA) is applied to building a high-quality mesh for a gas turbine. The compressible flow in the turbine is computed using the IGA and a stabilized method with improved discontinuity-capturing, weakly-enforced no-slip boundary-condition, and sliding-interface operators. The IGA results are compared with the results from the stabilized finite element simulation to reveal superior performance of the NURBS-based approach. Free-vibration analysis of the turbine rotor using the structural mechanics NURBS mesh is also carried out and shows that the NURBS mesh generation method can be used also in structural mechanics analysis. With the flow field from the NURBS-based turbine flow simulation, the Courant number is computed based on the NURBS mesh local length scale in the flow direction to show some of the other positive features of the mesh generation framework. The work presented further advances the IGA as a fully-integrated and robust design-to-analysis framework, and the IGA-based complex-geometry flow computation with moving boundaries and interfaces represents the first of its kind for compressible flows.

Variational multiscale methods and their precursors, stabilized methods, which are sometimes supplemented with discontinuity-capturing (DC) methods, have been playing their core-method role in flow computations increasingly with isogeometric discretization. The stabilization and DC parameters embedded in most of these methods play a significant role. The parameters almost always involve some local-length-scale expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, local-length-scale expressions originally intended for finite element discretization were being used also for isogeometric discretization. The direction-dependent expressions introduced in [Y. Otoguro, K. Takizawa and T. E. Tezduyar, Element length calculation in B-spline meshes for complex geometries, Comput. Mech. 65 (2020) 1085-1103, https://doi.org/10.1007/s00466-019-01809-w] target B-spline meshes for complex geometries. The key stages of deriving these expressions are mapping the direction vector from the physical element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. The expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. Element splitting may be a part of the computational method in a variety of cases, including computations with T-spline discretization and immersed boundary and extended finite element methods and their isogeometric versions. We do not want the element splitting to influence the actual discretization, which is represented by the control or nodal points. Therefore, the local length scale should be invariant with respect to element splitting. In element definition, invariance of the local length scale is a crucial requirement, because, unlike the element definition choices based on implementation convenience or computational efficiency, it influences the solution. We provide a proof, in the context of B-spline meshes, for the element-splitting invariance of the local-length-scale expressions introduced in the above reference.

Computational analysis of particle-laden-airflow erosion can help engineers have a better understanding of the erosion process, maintenance and protection of turbomachinery components. We present an integrated method for this class of computational analysis. The main components of the method are the residual-based Variational Multiscale (VMS) method, a finite element particle-cloud tracking (PCT) method with ellipsoidal clouds, an erosion model based on two time scales, and the Solid-Extension Mesh Moving Technique (SEMMT). The turbulent-flow nature of the analysis is addressed with the VMS, the particle-cloud trajectories are calculated based on the time-averaged computed flow field and closure models defined for the turbulent dispersion of particles, and one-way dependence is assumed between the flow and particle dynamics. Because the target-geometry update due to the erosion has a very long time scale compared to the fluid–particle dynamics, the update takes place in a sequence of “evolution steps” representing the impact of the erosion. A scale-up factor, calculated based on the update threshold criterion, relates the erosions and particle counts in the evolution steps to those in the PCT computation. As the target geometry evolves, the mesh is updated with the SEMMT. We present a computation designed to match the sand-erosion experiment we conducted with an aluminum-alloy target. We show that, despite the problem complexities and model assumptions involved, we have a reasonably good agreement between the computed and experimental data.

In computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction, moving-mesh methods enable mesh-resolution control near the interface and consequently high-resolution representation of the boundary layers. Good moving-mesh methods require good mesh moving methods. We introduce a low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state (ZSS). The method has been developed targeting isogeometric discretization but is also applicable to finite element discretization. With the large-deformation mechanics equations, we can expect to have a unique mesh associated with each step of the boundary or interface motion. With the fibers placed in multiple directions, we stiffen the element in those directions for the purpose of reducing the distortion during the mesh deformation. We optimize the ZSS by seeking orthogonality of the parametric directions, by mesh relaxation, and by making the ZSS time-dependent as needed. We present 2D and 3D test computations with isogeometric discretization. The computations show that the mesh moving method introduced performs well.

We address the computational challenges of and presents results from ventricle-valve-aorta flow analysis. Including the left ventricle (LV) in the model makes the flow into the valve, and consequently the flow into the aorta, anatomically more realistic. The challenges include accurate representation of the boundary layers near moving solid surfaces even when the valve leaflets come into contact, computation with high geometric complexity, anatomically realistic representation of the LV motion, and flow stability at the inflow boundary, which has a traction condition. The challenges are mainly addressed with a Space–Time (ST) method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method. The three special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The ST-discretization feature of the integrated method, ST-SI-TC-IGA, provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow in the LV, valve and aorta. The moving-mesh feature of the ST framework enables high-resolution computation near the leaflets. The ST-TC enables moving-mesh computation even with the TC created by the contact between the leaflets, dealing with the contact while maintaining high-resolution representation near the leaflets. The ST-IGA provides smoother representation of the LV, valve and aorta surfaces and increased accuracy in the flow solution. The ST-SI connects the separately generated LV, valve and aorta NURBS meshes, enabling easier mesh generation, connects the mesh zones containing the leaflets, enabling a more effective mesh moving, helps the ST-TC deal with leaflet–leaflet contact location change and contact sliding, and helps the ST-TC and ST-IGA keep the element density in the narrow spaces near the contact areas at a reasonable level. The ST-SI-TC-IGA is supplemented with two other special methods in this article. A structural mechanics computation method generates the LV motion from the CT scans of the LV and anatomically realistic values for the LV volume ratio. The Constrained-Flow-Profile (CFP) Traction provides flow stability at the inflow boundary. Test computation with the CFP Traction shows its effectiveness as an inflow stabilization method, and computation with the LV-valve-aorta model shows the effectiveness of the ST-SI-TC-IGA and the two supplemental methods.

Heart valve fluid–structure interaction (FSI) analysis is one of the computationally challenging cases in cardiovascular fluid mechanics. The challenges include unsteady flow through a complex geometry, solid surfaces with large motion, and contact between the valve leaflets. We introduce here an isogeometric sequentially-coupled FSI (SCFSI) method that can address the challenges with an outcome of high-fidelity flow solutions. The SCFSI analysis enables dealing with the fluid and structure parts individually at different steps of the solutions sequence, and also enables using different methods or different mesh resolution levels at different steps. In the isogeometric SCFSI analysis here, the first step is a previously computed (fully) coupled Immersogeometric Analysis FSI of the heart valve with a reasonable flow solution. With the valve leaflet and arterial surface motion coming from that, we perform a new, higher-fidelity fluid mechanics computation with the space–time topology change method and isogeometric discretization. Both the immersogeometric and space–time methods are variational multiscale methods. The computation presented for a bioprosthetic heart valve demonstrates the power of the method introduced.

Patient-specific computational flow analysis of coronary arteries with time-dependent medical-image data can provide valuable information to doctors making treatment decisions. Reliable computational analysis requires a good core method, high-fidelity space and time discretizations, and an anatomically realistic representation of the lumen motion. The space-time variational multiscale (ST-VMS) method has a good track record as a core method. The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the artery. The moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid-solid interfaces. The ST isogeometric analysis is a superior discretization method. With IGA basis functions in space, it enables more accurate representation of the lumen geometry and increased accuracy in the flow solution. With IGA basis functions in time, it enables a smoother representation of the lumen motion and a mesh motion consistent with that. With cubic NURBS in time, we obtain a continuous acceleration from the lumen-motion representation. Here we focus on making the lumen-motion representation anatomically realistic. We present a method to obtain from medical-image data in discrete form an anatomically realistic NURBS representation of the lumen motion, without sudden, unrealistic changes introduced by the higher-order representation. In the discrete projection from the medical-image data to the NURBS representation, we supplement the least-squares terms with two penalty terms, corresponding to the first and second time derivatives of the control-point trajectories. The penalty terms help us avoid the sudden unrealistic changes. The computation we present demonstrates the effectiveness of the method.

Computational flow analysis is now playing a key role in aerospace, energy and transportation technologies, bringing solution in challenging problems such as aerodynamics of parachutes, thermo-fluid analysis of ground vehicles and tires, and fluid–structure interaction (FSI) analysis of wind turbines. The computational challenges include complex geometries, moving boundaries and interfaces, FSI, turbulent flows, rotational flows, and large problem sizes. The Residual-Based Variational Multiscale (RBVMS), ALE-VMS and Space–Time VMS (ST-VMS) methods have been quite successful serving as core methods in addressing the computational challenges. The core methods are supplemented with special methods targeting specific classes of problems, such as the Slip Interface (SI) method, Multi-Domain Method, and the “ST-C” data compression method. We describe the core and special methods. We present, as examples of challenging computations performed with these methods, aerodynamic analysis of a ram-air parachute, thermo-fluid analysis of a freight truck and its rear set of tires, and aerodynamic and FSI analysis of two back-to-back wind turbines in atmospheric boundary layer flow.

Computational cardiovascular analysis can provide valuable information to cardiologists and cardiovascular surgeons on a patient-specific basis. There are many computational challenges that need to be faced in this class of flow analyses. They include highly unsteady flows, complex cardiovascular geometries, moving boundaries and interfaces, such as the motion of the heart valve leaflets, contact between moving solid surfaces, such as the contact between the leaflets, and the fluid–structure interaction between blood and cardiovascular structure. Many of these challenges have been or are being addressed by the Space–Time Variational Multiscale (ST-VMS) method, the Arbitrary Lagrangian–Eulerian VMS (ALE-VMS) method, and VMS-based immersogeometric analysis (IMGA-VMS), which serve as the core computational methods, and other special methods used in combination with them. We provide an overview of these methods and present examples of challenging computations carried out with them, including aortic and heart valve flow analyses. We also point out that these methods are general computational fluid dynamics techniques and have broad applicability to a wide range of other areas of science and engineering.

© 2020, The Author(s). We present computational flow analysis of a vertical-axis wind turbine (VAWT) that has been proposed to also serve as a tsunami shelter. In addition to the three-blade rotor, the turbine has four support columns at the periphery. The columns support the turbine rotor and the shelter. Computational challenges encountered in flow analysis of wind turbines in general include accurate representation of the turbine geometry, multiscale unsteady flow, and moving-boundary flow associated with the rotor motion. The tsunami-shelter VAWT, because of its rather high geometric complexity, poses the additional challenge of reaching high accuracy in turbine-geometry representation and flow solution when the geometry is so complex. We address the challenges with a space–time (ST) computational method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method, and mesh generation and improvement methods. The three special methods are the ST Slip Interface (ST-SI) method, ST Isogeometric Analysis (ST-IGA), and the ST/NURBS Mesh Update Method (STNMUM). The ST-discretization feature of the integrated method provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the blade and other turbine geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex turbine geometry. The quality of the mesh generated with this method is improved with a mesh relaxation method based on fiber-reinforced hyperelasticity and optimized zero-stress state. We present computations for the 2D and 3D cases. The computations show the effectiveness of our ST and mesh generation and relaxation methods in flow analysis of the tsunami-shelter VAWT.

© 2020, Springer Nature Switzerland AG. Many of the challenges encountered in computational analysis of wind turbines and turbomachinery are being addressed by the Arbitrary Lagrangian–Eulerian (ALE) and Space–Time (ST) Variational Multiscale (VMS) methods and isogeometric discretization. The computational challenges include turbulent rotational flows, complex geometries, moving boundaries and interfaces, such as the rotor motion, and the fluid–structure interaction (FSI), such as the FSI between the wind turbine blade and the air. The core computational methods are the ALE-VMS and ST-VMS methods. These are supplemented with special methods like the Slip Interface (SI) method and ST Isogeometric Analysis with NURBS basis functions in time. We describe the core and special methods and present, as examples of challenging computations performed, computational analysis of horizontal- and vertical-axis wind turbines and flow-driven string dynamics in pumps.

Variational multiscale methods, and their precursors, stabilized methods, have been playing a core-method role in semi-discrete and space-time (ST) flow computations for decades. These methods are sometimes supplemented with discontinuity-capturing (DC) methods. The stabilization and DC parameters embedded in most of these methods play a significant role. Various well-performing stabilization and DC parameters have been introduced in both the semi-discrete and ST contexts. The parameters almost always involve some element length expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, stabilization and DC parameters originally intended for finite element discretization were being used also for isogeometric discretization. Recently, element lengths and stabilization and DC parameters targeting isogeometric discretization were introduced for ST and semi-discrete computations, and these expressions are also applicable to finite element discretization. The key stages of deriving the direction-dependent element length expression were mapping the direction vector from the physical (ST or space-only) element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. Targeting B-spline meshes for complex geometries, we introduce here new element length expressions, which are outcome of a clear and convincing derivation and more suitable for element-level evaluation. The new expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. The test computations we present for advection-dominated cases, including 2D computations with complex meshes, show that the proposed element length expressions result in good solution profiles.

Variational multiscale methods, and their precursors, stabilized methods, have been very popular in flow computations in the past several decades. Stabilization parameters embedded in most of these methods play a significant role. The parameters almost always involve element length scales, most of the time in specific directions, such as the direction of the flow or solution gradient. We require the length scales, including the directional length scales, to have node-numbering invariance for all element types, including simplex elements. We propose a length scale expression meeting that requirement. We analytically evaluate the expression in the context of simplex elements and compared to one of the most widely used length scale expressions and show the levels of noninvariance avoided.

The space-time (ST) computational method "ST-SI-TC-IGA" has recently enabled computational analysis of tire aerodynamics with actual tire geometry, road contact and tire deformation. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). These ST methods played their parts in overcoming the computational challenges, including (i) the complexity of an actual tire geometry with longitudinal and transverse grooves, (ii) the spin of the tire, (iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, and (iv) the turbulent nature of the flow. The combination of the ST-VMS, ST-SI and the ST-IGA has also recently enabled solution of fluid film problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality. This was accomplished with the computational flexibility to go beyond the limitations of the Reynolds-equation model. Here we include and address the computational challenges associated with the road roughness and the fluid film between the tire and the road. The new methods we add to accomplish that include a remedy for the trapped fluid, a method for reducing the number of control points as a space occupied by the fluid shrinks down to a narrow gap, and a method for representing the road roughness. We present computations for a 2D test problem with a straight channel, a simple 2D model of the tire, and a 3D model with actual tire geometry and road roughness. The computations show the effectiveness of our integrated set of ST methods targeting tire aerodynamics.

Many of the computational challenges encountered in turbocharger-turbine flow analysis have been addressed by an integrated set of space-time (ST) computational methods. The core computational method is the ST variational multiscale (ST-VMS) method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST slip interface (ST-SI) method enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST Isogeometric Analysis enables more accurate representation of the turbine geometry and increased accuracy in the flow solution. The ST/NURBS Mesh Update Method enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex geometries involved. An SI also provides mesh generation flexibility in a general context by accurately connecting the two sides of the solution computed over nonmatching meshes, and that is enabling the use of nonmatching NURBS meshes in the computations. The computational analysis needs to cover a full intake/exhaust cycle, which is much longer than the turbine rotation cycle because of high rotation speeds, and the long duration required is an additional computational challenge. As one way of addressing that challenge, we propose here to calculate the turbine efficiency for the intake/exhaust cycle by interpolation from the efficiencies associated with a set of steady-inflow computations at different flow rates. The efficiencies obtained from the computations with time-dependent and steady-inflow representations of the intake/exhaust cycle compare well. This demonstrates that predicting the turbine performance from a set of steady-inflow computations is a good way of addressing the challenge associated with the multiple time scales.

Wind-turbine blade rain and sand erosion, over long periods of time, can degrade the aerodynamic performance and therefore the power production. Computational analysis of the erosion can help engineers have a better understanding of the maintenance and protection requirements. We present an integrated method for this class of computational analysis. The main components of the method are the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) stabilizations, a finite element particle-cloud tracking method, an erosion model based on two time scales, and the solid-extension mesh moving technique (SEMMT). The turbulent-flow nature of the analysis is handled with a Reynolds-averaged Navier-Stokes model and SUPG/PSPG stabilization, the particle-cloud trajectories are calculated based on the computed flow field and closure models defined for the turbulent dispersion of particles, and one-way dependence is assumed between the flow and particle dynamics. Because the geometry update due to the erosion has a very long time scale compared to the fluid-particle dynamics, the update takes place in a sequence of "evolution steps" representing the impact of the erosion. A scale-up factor, calculated in different ways depending on the update threshold criterion, relates the erosions and particle counts in the evolution steps to those in the fluid-particle simulation. As the blade geometry evolves, the mesh is updated with the SEMMT. We present computational analysis of rain and sand erosion for a wind-turbine blade strip, including a case with actual rainfall data and experimental aerodynamic data for eroded airfoil geometries.

This is the first part of a two-part article on computer modeling of wind turbines. We describe the recent advances made by our teams in ALE-VMS and ST-VMS computational aerodynamic and fluid-structure interaction (FSI) analysis of wind turbines. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian-Eulerian method. The VMS components are from the residual-based VMS method. The ST-VMS method is the VMS version of the Deforming-Spatial-Domain/Stabilized Space-Time method. The ALE-VMS and ST-VMS serve as the core methods in the computations. They are complemented by special methods that include the ALE-VMS versions for stratified flows, sliding interfaces and weak enforcement of Dirichlet boundary conditions, ST Slip Interface (ST-SI) method, NURBS-based isogeometric analysis, ST/NURBS Mesh Update Method (STNMUM), Kirchhoff-Love shell modeling of wind-turbine structures, and full FSI coupling. The VMS feature of the ALE-VMS and ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow, and the moving-mesh feature of the ALE and ST frameworks enables high-resolution computation near the rotor surface. The ST framework, in a general context, provides higher-order accuracy. The ALE-VMS version for sliding interfaces and the ST-SI enable moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the sliding interface or the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-SI also enables prescribing the fluid velocity at the turbine rotor surface as weakly-enforced Dirichlet boundary condition. The STNMUM enables exact representation of the mesh rotation. The analysis cases reported include both the horizontal-axis and vertical-axis wind turbines, stratified and unstratified flows, standalone wind turbines, wind turbines with tower or support columns, aerodynamic interaction between two wind turbines, and the FSI between the aerodynamics and structural dynamics of wind turbines. Comparisons with experimental data are also included where applicable. The reported cases demonstrate the effectiveness of the ALE-VMS and ST-VMS computational analysis in wind-turbine aerodynamics and FSI.

Because the medical-image-based geometries used in patient-specific arterial fluid-structure interaction computations do not come from the zero-stress state (ZSS) of the artery, we need to estimate the ZSS required in the computations. The task becomes even more challenging for arteries with complex geometries, such as the aorta. In a method we introduced earlier the estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and fewer elements. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. The method has two main components. 1. An iteration technique, which starts with a calculated ZSS initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the medical-image-based target shape is matched. 2. A design procedure, which is based on the Kirchhoff-Love shell model of the artery, is used for calculating the ZSS initial guess. Here we increase the scope and robustness of the method by introducing a new design procedure for the ZSS initial guess. The new design procedure has two features. (a) An IPB shell-like coordinate system, which increases the scope of the design to general parametrization in the computational space. (b) Analytical solution of the force equilibrium in the normal direction, based on the Kirchhoff-Love shell model, which places proper constraints on the design parameters. This increases the estimation accuracy, which in turn increases the robustness of the iterations and the convergence speed. To show how the new design procedure for the ZSS initial guess performs, we first present 3D test computations with a straight tube and a Y-shaped tube. Then we present a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in the model.

The image-based arterial geometries used in patient-specific arterial fluid-structure interaction (FSI) computations, such as aorta FSI computations, do not come from the zero-stress state (ZSS) of the artery. We propose a method for estimating the ZSS required in the computations. Our estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The method has two main components. (1) An iterative method, which starts with a calculated initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the image-based target shape is matched. (2) A method, which is based on the shell model of the artery, is used for calculating the initial guess. The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. Calculating the initial guess based on the shell model of the artery results in a more realistic initial guess. To show how the new ZSS estimation method performs, we first present 3D test computations with a Y-shaped tube. Then we show a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in our model.

Tire aerodynamics with actual tire geometry, road contact and tire deformation pose tough computational challenges. The challenges include (1) the complexity of an actual tire geometry with longitudinal and transverse grooves, (2) the spin of the tire, (3) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact and tire deformation, and (4) the turbulent nature of the flow. A new space-time (ST) computational method, ST-SI-TC-IGA, is enabling us to address these challenges. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). The VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid-solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-SI enables moving-mesh computation with the tire spinning. The mesh covering the tire spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-TC enables moving-mesh computation even with the TC created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire. Integration of the ST-SI and ST-TC enables high-resolution representation even though parts of the SI are coinciding with the tire and road surfaces. It also enables dealing with the tire-road contact location change and contact sliding. By integrating the ST-IGA with the ST-SI and ST-TC, in addition to having a more accurate representation of the tire geometry and increased accuracy in the flow solution, the element density in the tire grooves and in the narrow spaces near the contact areas is kept at a reasonable level. We present computations with the ST-SI-TC-IGA and two models of flow around a rotating tire with road contact and prescribed deformation. One is a simple 2D model for verification purposes, and one is a 3D model with an actual tire geometry and a deformation pattern provided by the tire company. The computations show the effectiveness of the ST-SI-TC-IGA in tire aerodynamics.

In this lead paper of the special issue, we provide a brief summary of the stabilized and multiscale methods in fluid dynamics. We highlight the key features of the stabilized and multiscale scale methods, and variational methods in general, that make these approaches well suited for computational analysis of complex, unsteady flows encountered in modern science and engineering applications. We mainly focus on the recent developments. We discuss application of the variational multiscale (VMS) methods to fluid dynamics problems involving computational challenges associated with high-Reynolds-number flows, wall-bounded turbulent flows, flows on moving domains including subdomains in relative motion, fluid-structure interaction (FSI), and complex-fluid flows with FSI.

We present a space-time (ST) computational flow analysis method with built-in Reynolds-equation limit. The method enables solution of lubrication fluid dynamics problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality, but with the computational flexibility to go beyond the limitations of the Reynolds-equation model. The key components of the method are the ST Variational Multiscale (ST-VMS) method, ST Isogeometric Analysis (ST-IGA), and the ST Slip Interface (ST-SI) method. The VMS feature of the ST-VMS serves as a numerical stabilization method with a good track record, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid-solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-IGA enables more accurate representation of the solid-surface geometries and increased accuracy in the flow solution in general. With the ST-IGA, even with just one quadratic NURBS element across the gap of the lubrication fluid dynamics problem, we reach a solution quality comparable to that of the Reynolds-equation model. The ST-SI enables moving-mesh computation when the spinning solid surface is noncircular. The mesh covering the solid surface spins with it, retaining the high-resolution representation of the flow near the surface, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. We present detailed 2D test computations to show how the method performs compared to the Reynolds-equation model, compared to finite element discretization, at different circumferential and normal mesh refinement levels, when there is an SI in the mesh, and when the no-slip boundary conditions are weakly-enforced.

We present methods for computation of flow-driven string dynamics in a pump and related residence time. The string dynamics computations help us understand how the strings carried by a fluid interact with the pump surfaces, including the blades, and get stuck on or around those surfaces. The residence time computations help us to have a simplified but quick understanding of the string behavior. The core computational method is the Space-Time Variational Multiscale (ST-VMS) method, and the other key methods are the ST Isogeometric Analysis (ST-IGA), ST Slip Interface (ST-SI) method, ST/NURBS Mesh Update Method (STNMUM), a general-purpose NURBS mesh generation method for complex geometries, and a one-way-dependence model for the string dynamics. The ST-IGA with NURBS basis functions in space is used in both fluid mechanics and string structural dynamics. The ST framework provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the turbulent nature of the unsteady flow, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the pump geometry and increased accuracy in the flow solution. The IGA discretization also enables increased accuracy in the structural dynamics solution, as well as smoothness in the string shape and fluid dynamics forces computed on the string. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometry we have here. With the one-way-dependence model, we compute the influence of the flow on the string dynamics, while avoiding the formidable task of computing the influence of the string on the flow, which we expect to be small.

Computational fluid-structure interaction (FSI) and flow analysis now have a significant role in design and performance evaluation of turbomachinery systems, such as wind turbines, fans, and turbochargers. With increasing scope and fidelity, computational analysis can help improve the design and performance. For example, it can help add a passive morphing attachment (MA) to the blades of an axial fan for the purpose of controlling the blade load and section stall. We present a stabilized Arbitrary Lagrangian-Eulerian (ALE) method for computational FSI analysis of passive morphing in turbomachinery. The main components of the method are the Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) stabilizations in the ALE framework, mesh moving with Jacobian-based stiffening, and block-iterative FSI coupling. The turbulent-flow nature of the analysis is handled with a Reynolds-Averaged Navier-Stokes (RANS) model and SUPG/PSPG stabilization, supplemented with the "DRDJ" stabilization. As the structure moves, the fluid mechanics mesh moves with the Jacobian-based stiffening method, which reduces the deformation of the smaller elements placed near the solid surfaces. The FSI coupling between the blocks of the fully-discretized equation system representing the fluid mechanics, structural mechanics, and mesh moving equations is handled with the block-iterative coupling method. We present two-dimensional (2D) and three-dimensional (3D) computational FSI studies for an MA added to an axial-fan blade. The results from the 2D study are used in determining the spanwise length of the MA in the 3D study.

In an article published online in July 2018 it was stated that the algorithm proposed in the article is enabling practical implementation of the space-time FEM for engineering applications. In fact, space-time computations in practical engineering applications were already enabled in 1993. We summarize the computations that have taken place since then. These computations started with finite element discretization and are now also with isogeometric discretization. They were all in 3D space and were all carried out on parallel computers. For quarter of a century, these computations brought solution to many classes of complex problems ranging from Orion spacecraft parachutes to wind turbines, from patient-specific cerebral aneurysms to heart valves, from thermo-fluid analysis of ground vehicles and tires to turbocharger turbines and exhaust manifolds.

We derive a hyperelastic shell formulation based on the Kirchhoff-Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid-structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the midsurface location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the midsurface location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung's models, for the compressible- and incompressible-material cases, and for two different locations of the midsurface. We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.

One of the challenges in computational fluid-structure interaction (FSI) analysis of spacecraft parachutes is the geometric porosity, a design feature created by the hundreds of gaps and slits that the flow goes through. Because FSI analysis with resolved geometric porosity would be exceedingly time-consuming, accurate geometric-porosity modeling becomes essential. The geometric-porosity model introduced earlier in conjunction with the space-time FSI method enabled successful computational analysis and design studies of the Orion spacecraft parachutes in the incompressible-flow regime. Recently, porosity models and ST computational methods were introduced, in the context of finite element discretization, for compressible-flow aerodynamics of parachutes with geometric porosity. The key new component of the ST computational framework was the compressible-flow ST slip interface method, introduced in conjunction with the compressible-flow ST SUPG method. Here, we integrate these porosity models and ST computational methods with isogeometric discretization. We use quadratic NURBS basis functions in the computations reported. This gives us a parachute shape that is smoother than what we get from a typical finite element discretization. In the flow analysis, the combination of the ST framework, NURBS basis functions, and the SUPG stabilization assures superior computational accuracy. The computations we present for a drogue parachute show the effectiveness of the porosity models, ST computational methods, and the integration with isogeometric discretization.

© Published under licence by IOP Publishing Ltd. We present computational analysis of flow-driven string dynamics in a pump and the related residence time calculation. The objective in the study is to understand how the strings carried by a fluid interact with the pump surfaces, including the blades, and get stuck on or around those surfaces. The residence time calculations help us to have a simplified but quick understanding of the string behavior. The core computational method is the Space-Time Variational Multiscale (ST-VMS) method, and the other key methods are the ST Isogeometric Analysis (ST-IGA), ST Slip Interface (ST-SI) method, ST/NURBS Mesh Update Method (STNMUM), a general-purpose NURBS mesh generation method for complex geometries, and a one-way-dependence model for the string dynamics. The ST-IGA with NURBS basis functions in space is used in both fluid mechanics and string structural dynamics. The ST framework provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the turbulent nature of the unsteady flow, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the pump geometry and increased accuracy in the flow solution. The IGA discretization also enables increased accuracy in the structural dynamics solution, as well as smoothness in the string shape and fluid dynamics forces computed on the string. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometry. With the one-way-dependence model, we compute the influence of the flow on the string dynamics, while avoiding the formidable task of computing the influence of the string on the flow, which we expect to be small.

We address the computational challenges encountered in turbocharger turbine and exhaust manifold flow analysis. The core computational method is the Space-Time Variational Multiscale (ST-VMS) method, and the other key methods are the ST Isogeometric Analysis (ST-IGA), ST Slip Interface (ST-SI) method, ST/NURBS Mesh Update Method (STNMUM), and a general-purpose NURBS mesh generation method for complex geometries. The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the manifold and turbine, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the turbine and manifold geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometries we have here. An SI also provides mesh generation flexibility in a general context by accurately connecting the two sides of the solution computed over nonmatching meshes. That is enabling us to use nonmatching NURBS meshes here. Stabilization parameters and element length definitions play a significant role in the ST-VMS and ST-SI. For the ST-VMS, we use the stabilization parameters introduced recently, and for the ST-SI, the element length definition we are introducing here. The model we actually compute with includes the exhaust gas purifier, which makes the turbine outflow conditions more realistic. We compute the flow for a full intake/exhaust cycle, which is much longer than the turbine rotation cycle because of high rotation speeds, and the long duration required is an additional computational challenge. The computation demonstrates that the methods we use here are very effective in this class of challenging flow analyses. (C) 2018 The Authors. Published by Elsevier Ltd.

We present detailed studies on mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization. Both factors play a key role in the reliability and practical value of aorta flow analysis. The core computational method is the space-time Variational Multiscale (ST-VMS) method. The other key method is the ST Isogeometric Analysis (ST-IGA). The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the aorta. The ST-IGA provides smoother representation of the aorta and increased accuracy in the flow solution. We conduct the studies for a patient-specific aorta geometry. We determine the level of mesh refinement needed and assess the nature of the flow periodicity reached. (C) 2018 Elsevier Ltd. All rights reserved.

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

We present our computational methods for and results from aorta flow analysis and heart valve flow and structure analysis. In flow analysis, the core method is the space–time Variational Multiscale (ST-VMS) method. The other key methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flows in the aorta and heart valve. The moving-mesh feature of the ST framework enables high-resolution computation near the valve leaflets. The ST-SI connects the sectors of meshes containing the leaflets, enabling a more effective mesh moving. The ST-TC enables moving-mesh computation even with the TC created by the contact between the leaflets. It deals with the contact while maintaining high-resolution representation near the leaflets. Integration of the ST-SI and ST-TC enables high-resolution representation even though parts of the SI are coinciding with the leaflet surfaces. It also enables dealing with leaflet–leaflet contact location change and contact sliding. The ST-IGA provides smoother representation of aorta and valve surfaces and increased accuracy in the flow solution. With the integration of the ST-IGA with the ST-SI and ST-TC, the element density in the narrow spaces near the contact areas is kept at a reasonable level. In structure analysis, we use a Kirchhoff–Love shell model, where we take the stretch in the third direction into account in calculating the curvature term. The computations presented demonstrate the scope and effectiveness of the methods.

© 2018, Springer Nature Switzerland AG. Spatial discretization with NURBS meshes is increasingly being used in computational analysis, including computational flow analysis with complex geometries. In flow analysis, compared to standard discretization methods, isogeometric discretization provides more accurate representation of the solid surfaces and increased accuracy in the flow solution. The Space-Time Computational Analysis (STCA), where the core method is the ST Variational Multiscale method, is increasingly relying on the ST Isogeometric Analysis (ST-IGA) as one of its key components, quite often also with IGA basis functions in time. The ST Slip Interface (ST-SI) and ST Topology Change methods are two other key components of the STCA, and complementary nature of all these ST methods makes the STCA powerful and practical. To make the ST-IGA use, and in a wider context the IGA use, even more practical in computational flow analysis with complex geometries, NURBS volume mesh generation needs to be easier and more automated. To that end, we present a general-purpose NURBS mesh generation method. The method is based on multi-block-structured mesh generation with existing techniques, projection of that mesh to a NURBS mesh made of patches that correspond to the blocks, and recovery of the original model surfaces to the extent they are suitable for accurate and robust fluid mechanics computations. It is expected to retain the refinement distribution and element quality of the multi-block-structured mesh that we start with. The flexibility of discretization with the general-purpose mesh generation is supplemented with the ST-SI method, which allows, without loss of accuracy, C−1 continuity between NURBS patches and thus removes the matching requirement between the patches. We present mesh-quality performance studies for 2D and 3D meshes, including those for complex models, and test computation for a turbocharger turbine and exhaust manifold. These demonstrate that the general-purpose mesh generation method proposed makes the IGA use in computational flow analysis even more practical.

We present a heart valve flow computation with the Space-Time Slip Interface Topology Change (ST-SI-TC) method and Isogeometric Analysis (IGA). The computation is for a realistic heart valve model with actual contact between the valve leaflets. The ST-SI-TC method integrates the ST-SI and ST-TC methods in the framework of the ST Variational Multiscale (ST-VMS) method. The STVMS method functions as a moving-mesh method, which maintains high-resolution boundary layer representation near the solid surfaces. The ST-TC method was introduced for moving-mesh computation of flow problems with TC, such as contact between the leaflets of a heart valve. It deals with the contact while maintaining highresolution representation near the leaflet surfaces. The ST-SI method was originally introduced to addresses the challenge involved in high-resolution representation of the boundary layers near spinning solid surfaces. The mesh covering a spinning solid surface spins with it, and the SI between that mesh and the rest of the mesh accurately connects the two sides. This maintains the high-resolution representation near solid surfaces. In the context of heart valves, the SI connects the sectors of meshes containing the leaflets, enabling a more effective mesh moving. In that context, the ST-SI-TC method enables high-resolution representation even when the contact is between leaflets that are covered by meshes with SI. It also enables dealing with contact location change or contact and sliding on the SI. With IGA, in addition to having a more accurate representation of the surfaces and increased accuracy in the flow solution, the element density in the narrow spaces near the contact areas is kept at a reasonable level. Furthermore, because the flow representation in the contact area has a wider support in IGA, the flow computation method becomes more robust. The computation we present for an aortic-valve model shows the effectiveness of the ST-SI-TC-IGA method.

In patient-specific arterial fluid-structure interaction computations the image-based arterial geometry does not come from a zero-stress state (ZSS), requiring an estimation of the ZSS. A method for estimation of element-based ZSS (EBZSS) was introduced earlier in the context of finite element wall discretization. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the “opening angle.” 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we introduce the version of the EBZSS estimation method with isogeometric wall discretization. With NURBS basis functions, we may be able to use larger elements, consequently less number of elements, compared to linear basis functions. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we present 2D test computations with straight-tube configurations.

The Space-Time Computational Analysis (STCA) with key components that include the ST Variational Multiscale (ST-VMS) method and ST Isogeometric Analysis (ST-IGA) is being increasingly used in fluid mechanics computations with complex geometries. In such computations, the ST-VMS serves as the core method, complemented by the ST-IGA, and sometimes by additional key components, such as the ST Slip Interface (ST-SI) method. To make the ST-IGA use, and in a wider context the IGA use, even more practical in fluid mechanics computations, NURBS volume mesh generation needs to be easier and as automated as possible. To that end, we present a general-purpose NURBS mesh generation method. The method is based on multi-block structured mesh generation with existing techniques, projection of that mesh to a NURBS mesh made of patches that correspond to the blocks, and recovery of the original model surfaces to the extent they are suitable for accurate and robust fluid mechanics computations. It is expected to retain the refinement distribution and element quality of the multi-block structured mesh that we start with. The flexibility of discretization with the general-purpose mesh generation is supplemented with the ST-SI method, which allows, without loss of accuracy, C-1 continuity between NURBS patches and thus removes the matching requirement between the patches. We present a test computation for a turbocharger turbine and exhaust manifold, which demonstrates that the general-purpose mesh generation method proposed makes the IGA use in fluid mechanics computations even more practical. (C) 2017 Elsevier Ltd. All rights reserved.

Heart valve flow computation requires accurate representation of boundary layers near moving solid surfaces, including the valve leaflet surfaces, even when the leaflets come into contact. It also requires dealing with a high level of geometric complexity. We address these computational challenges with a Space-Time (ST) method developed by integrating three special ST methods in the framework of the ST Variational Multiscale (ST-VMS) method. The special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The computations are for a realistic aortic-valve model with prescribed valve leaflet motion and actual contact between the leaflets. The ST-VMS method functions as a moving-mesh method, which maintains high-resolution boundary layer representation near the solid surfaces, including leaflet surfaces. The ST-TC method was introduced for moving-mesh computation of flow problems with TC, such as contact between the leaflets of a heart valve. It deals with the contact while maintaining high-resolution representation near the leaflet surfaces. The ST-SI method was originally introduced to have high-resolution representation of the boundary layers near spinning solid surfaces. The mesh covering a spinning solid surface spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides. In the context of heart valves, the SI connects the sectors of meshes containing the leaflets, enabling a more effective mesh moving. In that context, integration of the ST-SI and ST-TC methods enables high-resolution representation even when the contact is between leaflets that are covered by meshes with SI. It also enables dealing with contact location change or contact and sliding on the SI. By integrating the ST-IGA with the ST-SI and ST-TC methods, in addition to having a more accurate representation of the surfaces and increased accuracy in the flow solution, the element density in the narrow spaces near the contact areas is kept at a reasonable level. Furthermore, because the flow representation in the contact area has a wider support in IGA, the flow computation method becomes more robust. The computations we present for an aortic-valve model with two different modes of prescribed leaflet motion show the effectiveness of the ST-SI-TC-IGA method. (C) 2016 Elsevier Ltd. All rights reserved.

Spacecraft-parachute designs quite often include "geometric porosity" created by the hundreds of gaps and slits that the flow goes through. Computational fluid-structure interaction (FSI) analysis of these parachutes with resolved geometric porosity would be exceedingly challenging, and therefore accurate modeling of the geometric porosity is essential for reliable FSI analysis. The space-time FSI (STFSI) method with the homogenized modeling of geometric porosity has proven to be reliable in computational analysis and design studies of Orion spacecraft parachutes in the incompressible-flow regime. Here we introduce porosity models and ST computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. The main components of the ST computational framework we use are the compressible-flow ST SUPG method, which was introduced earlier, and the compressible-flow ST Slip Interface method, which we introduce here. The computations we present for a drogue parachute show the effectiveness of the porosity models and ST computational methods.

Patient-specific arterial fluid-structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the "opening angle." 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight-tube configurations. Then we show how the method can be used in a 3D computation where the target geometry is coming from medical image of a human aorta.

We focus on turbocharger computational flow analysis with a method that possesses higher accuracy in spatial and temporal representations. In the method we have developed for this purpose, we use a combination of (i) the Space-Time Variational Multiscale (ST-VMS) method, which is a stabilized formulation that also serves as a turbulence model, (ii) the ST Slip Interface (ST-SI) method, which maintains high-resolution representation of the boundary layers near spinning solid surfaces by allowing in a consistent fashion slip at the interface between the mesh covering a spinning surface and the mesh covering the rest of the domain, and (iii) the Isogeometric Analysis (IGA), where we use NURBS basis functions in space and time. The basis functions are spatially higher-order in all representations, and temporally higher-order in representation of the solid-surface and mesh motions. The ST nature of the method gives us higher-order accuracy in the flow solver, and when combined with temporally higher-order basis functions, a more accurate representation of the surface motion, and a mesh motion consistent with that. The spatially higher-order basis functions give us again higher-order accuracy in the flow solver, a more accurate, in some parts exact, representation of the surface geometry, and better representation in evaluating the second-order spatial derivatives. Using NURBS basis functions with a complex geometry is not trivial, however, once we generate the mesh, the computational efficiency is substantially increased. We focus on the turbine part of a turbocharger, but our method can also be applied to the compressor part and thus can be extended to the full turbocharger. (C) 2016 Elsevier Ltd. All rights reserved.

We focus on computational analysis of flow-driven string dynamics. The objective is to understand how the strings carried by a fluid interact with the solid surfaces present and get stuck on or around those surfaces. Our target application is turbomachinery, such as understanding how strings get stuck on or around the blades of a fan. The components of the method we developed for this purpose are the Space-Time Variational Multiscale (ST-VMS) and ST Slip Interface (ST-SI) methods for the fluid dynamics, and a one-way-dependence model and the Isogeometric Analysis (IGA) for the string dynamics. The ST-VMS method is the core computational technology and it also has the features of a turbulence model. The ST-SI method allows in a consistent fashion slip at the interface between the mesh covering a spinning solid surface and the mesh covering the rest of the domain, and with this, we maintain high-resolution representation of the boundary layers near spinning solid surfaces such as fan blades. With the one-way-dependence model, we compute the influence of the flow on the string dynamics, while avoiding the formidable task of computing the influence of the string on the flow, which we expect to be small. The IGA for the string dynamics gives us not only a higher-order method and smoothness in the structure shape, but also smoothness in the fluid dynamics forces calculated on the string. To demonstrate how the method can be used in computational analysis of flow-driven string dynamics, we present the pilot computations we carried out, for a duct with cylindrical obstacles and for a ventilating fan. (C) 2016 Elsevier Ltd. All rights reserved.

The Space-Time Variational Multiscale(ST-VMS) method was introduced to function as a moving-mesh method. It is the VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method. It has reasonably good turbulence modeling features and serves as a core computational method. The ST Slip Interface (ST-SI) method was introduced to addresses the challenge involved in high-resolution representation of the boundary layers near spinning solid surfaces. The mesh covering a spinning solid surface spins with it and thus maintains the high-resolution representation near it. The ST-TC method was introduced for moving-mesh computation of flow problems with topology changes, such as contact between solid surfaces. It deals with the TC while maintaining high-resolution boundary layer representation near solid surfaces. The "ST-SI-TC" method we introduce here integrates the ST-SI and ST-TC methods in the ST-VMS framework. It enables accurate flow analysis when we have a spinning solid surface that is in contact with a solid surface. We present two test computations with the ST-SI-TC method, and they are both with models of flow around a rotating tire with road contact and prescribed deformation, one with a 2D model, and one with a 3D model. (C) 2016 Elsevier Ltd. All rights reserved.

We present a method for structural and fluid mechanics computations of ram-air parachutes. A ram-air parachute is a parafoil inflated by the airflow through the inlets at the leading edge. It has better control and gliding capability than round parachutes. Reliable analysis of ram-air parachutes requires accurate representation of the parafoil geometry, fabric porosity and the complex, multiscale flow behavior involved in this class of problems. The key components of the method are (i) the Space-Time Variational Multiscale (ST-VMS) method, (ii) the version of the ST Slip Interface (ST-SI) method where the SI is between a thin porous structure and the fluid on its two sides, (iii) the ST Isogeometric Analysis (ST-IGA), and (iv) special-purpose NURBS mesh generation techniques for the parachute structure and the flow field inside and outside the parafoil. The ST-VMS method is a stabilized formulation that also serves as a turbulence model and can deal effectively with the complex, multiscale flow behavior. With the STSI version for porosity modeling, we deal with the fabric porosity in a fashion consistent with how we deal with the standard SIs and how we enforce the Dirichlet boundary conditions weakly. The ST-IGA, with NURBS basis functions in space, gives us, with relatively few number of unknowns, accurate representation of the parafoil geometry and increased accuracy in the flow solution. The special-purpose mesh generation techniques enable NURBS representation of the structure and fluid domains with significant geometric complexity. The test computations we present are for building a starting parachute shape and a starting flow field associated with that parachute shape, which are the first two key steps in fluid-structure interaction analysis. The computations demonstrate the effectiveness of the method in this class of problems. (C) 2016 Elsevier Ltd. All rights reserved.

Wind-turbine blade rain erosion damage could be significant if the blades are not protected. This damage would not typically influence the structural integrity of the blades, but it could degrade the aerodynamic performance and therefore the power production. We present computational analysis of rain erosion in wind-turbine blades. The main components of the method used in the analysis are the Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) stabilizations, a finite element particle-cloud tracking method, and an erosion model. The turbulent-flow nature of the analysis is handled with a RANS model and SUPG/PSPG stabilization, the particle-cloud trajectories are calculated based on the computed flow field and closure models defined for the turbulent dispersion of particles, and one-way dependence is assumed between the flow and particle dynamics. The erosion patterns are then computed based on the particle-cloud data. The patterns are consistent with those observed in the actual wind turbines. (C) 2016 Elsevier Ltd. All rights reserved.

We present computational thermo-fluid analysis of a disk brake, including thermo-fluid analysis of the flow around the brake and heat conduction analysis of the disk. The computational challenges include proper representation of the small-scale thermo-fluid behavior, high-resolution representation of the thermo-fluid boundary layers near the spinning solid surfaces, and bringing the heat transfer coefficient (HTC) calculated in the thermo-fluid analysis of the flow to the heat conduction analysis of the spinning disk. The disk brake model used in the analysis closely represents the actual configuration, and this adds to the computational challenges. The components of the method we have developed for computational analysis of the class of problems with these types of challenges include the Space-Time Variational Multiscale method for coupled incompressible flow and thermal transport, ST Slip Interface method for high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces, and a set of projection methods for different parts of the disk to bring the HTC calculated in the thermo-fluid analysis. With the HTC coming from the thermo-fluid analysis of the flow around the brake, we do the heat conduction analysis of the disk, from the start of the breaking until the disk spinning stops, demonstrating how the method developed works in computational analysis of this complex and challenging problem.

Wind-turbine blades exposed to rain can be damaged by erosion if not protected. Although this damage does not typically influence the structural response of the blades,it could heavily degrade the aerodynamic performance,and therefore the power production. We present a method for computational analysis of rain erosion in wind-turbine blades. The method is based on a stabilized finite element fluid mechanics formulation and a finite element particle-cloud tracking method. Accurate representation of the flow would be essential in reliable computational turbomachinery analysis and design. The turbulent-flow nature of the problem is dealt with a RANS model and SUPG/PSPG stabilization,the particle-cloud trajectories are calculated based on the flow field and closure models for the turbulence-particle interaction,and one-way dependence is assumed between the flow field and particle dynamics. The erosion patterns are then computed based on the particle-cloud data.

This is an overview of some of the new directions we have taken the space-time (ST) computational methods since 2010 in bringing solution and analysis to different classes of challenging engineering problems. The new directions include the variational multiscale (VMS) version of the Deforming-Spatial-Domain/Stabilized ST method,using NURBS basis functions in temporal representation of the unknown variables and motion of the solid surfaces and fluid mechanics meshes,ST techniques with continuous representation in time,ST interface-tracking with topology change,and the ST-VMS method for flow computations with slip interfaces. We describe these new directions and present a few examples.

This chapter is on fluid-structure interaction (FSI) analysis of blood flow in the thoracic aorta. The FSI is handled with the Sequentially Coupled Arterial FSI technique. We focus on the relationship between the aorta centerline geometry and the wall shear stress (WSS) distribution. The model centerlines are extracted from the CT scans,and we assume a constant diameter for the artery segment. Then,torsion-free model geometries are generated by projecting the original centerline to its averaged plane of curvature. The WSS distributions for the original and projected geometries are compared to examine the influence of the torsion.

We present the space-time variational multiscale (ST-VMS) method for flow computations with slip interfaces (ST-SI). The method is intended for fluid-structure interaction (FSI) analysis where one or more of the subdomains contain spinning structures, such as the rotor of a wind turbine, and the subdomains are covered by meshes that do not match at the interface and have slip between them. The mesh covering a subdomain with the spinning structure spins with it, thus maintaining the high-resolution representation of the boundary layers near the structure. The starting point in the development of the method is the version of the arbitrary Lagrangian-Eulerian VMS (ALE-VMS) method designed for computations with "sliding interfaces". Interface terms similar to those in the ALE-VMS version are added to the ST-VMS formulation to account for the compatibility conditions for the velocity and stress. In addition to having a high-resolution representation of the boundary layers, because the ST framework allows NURBS functions in temporal representation of the structure motion, we have exact representation of the circular paths associated with the spinning. The ST-SI method includes versions for cases where the SI is between fluid and solid domains with weakly-imposed Dirichlet conditions for the fluid and for cases where the SI is between a thin porous structure and the fluid on its two sides. Test computations with 2D and 3D models of a vertical-axis wind turbine show the effectiveness of the ST-SI method.

In this paper, we provide a brief overview of the development of stabilized and multiscale methods in fluid dynamics. We mainly focus on recent developments and new directions in the variational multiscale (VMS) methods. We also discuss applications of the VMS techniques to fluid dynamics problems involving computational challenges associated with high-Reynolds-number flows, wall-bounded turbulent flows, flows with moving domains including subdomains in relative motion, and free-surface flows.

We present the core and special multiscale space-time (ST) methods we developed for thermo-fluid analysis of a ground vehicle and its tires. We also present application of these methods to thermo-fluid analysis of a freight truck and its rear set of tires. The core multiscale ST method is the ST variational multiscale (ST-VMS) formulation of the Navier-Stokes equations of incompressible flows with thermal coupling, which is multiscale in the way the small-scale thermo-fluid behavior is represented in the computations. The special multiscale ST method is spatially multiscale, where the thermo-fluid computation over the global domain with a reasonable mesh refinement is followed by a higher-resolution computation over the local domain containing the rear set of tires, with the boundary and initial conditions coming from the data computed over the global domain. The large amount of time-history data from the global computation is stored using the ST computation technique with continuous representation in time (ST-C), which serves as a data compression technique in this context. In our thermo-fluid analysis, we use a road-surface temperature higher than the free-stream temperature, and a tire-surface temperature that is even higher. We also include in the analysis the heat from the engine and exhaust system, with a reasonably realistic representation of the rate by which that heat transfer takes place as well as the surface geometry of the engine and exhaust system over which the heat transfer occurs. We take into account the heave motion of the truck body. We demonstrate how the spatially multiscale ST method, with higher-refinement mesh in the local domain, substantially increases the accuracy of the computed heat transfer rates from the tires.

The space-time fluid-structure interaction (STFSI) methods for 3D parachute modeling are now at a level where they can bring reliable, practical analysis to some of the most complex parachute systems, such as spacecraft parachutes. The methods include the Deforming-Spatial-Domain/Stabilized ST method as the core computational technology, and a good number of special FSI methods targeting parachutes. Evaluating the stability characteristics of a parachute based on how the aerodynamic moment varies as a function of the angle of attack is one of the practical analyses that reliable parachute FSI modeling can deliver. We describe the special FSI methods we developed for this specific purpose and present the aerodynamic-moment data obtained from FSI modeling of NASA Orion spacecraft parachutes and Japan Aerospace Exploration Agency (JAXA) subscale parachutes.

Computational analysis of flapping-wing aerodynamics with wing clapping was one of the classes of computations targeted in introducing the space-time (ST) interface-tracking method with topology change (ST-TC). The ST-TC method is a new version of the deforming-spatial-domain/stabilized ST (DSD/SST) method, enhanced with a master-slave system that maintains the connectivity of the "parent" fluid mechanics mesh when there is contact between the moving interfaces. With that enhancement and because of its ST nature, the ST-TC method can deal with an actual contact between solid surfaces in flow problems with moving interfaces. It accomplishes that while still possessing the desirable features of interface-tracking (moving-mesh) methods, such as better resolution of the boundary layers. Earlier versions of the DSD/SST method, with effective mesh update, were already able to handle moving-interface problems when the solid surfaces are in near contact or create near TC. Flapping-wing aerodynamics of an actual locust, with the forewings and hindwings crossing each other very close and creating near TC, is an example of successfully computed problems. Flapping-wing aerodynamics of a micro aerial vehicle (MAV) with the wings of an actual locust is another example. Here we show how the ST-TC method enables 3D computational analysis of flapping-wing aerodynamics of an MAV with wing clapping. In the analysis, the wings are brought into an actual contact when they clap. We present results for a model dragonfly MAV.

The space-time fluid-structure interaction (STFSI) methods for parachute modeling are now capable of bringing reliable analysis to spacecraft parachutes, which pose formidable computational challenges. A number of special FSI methods targeting spacecraft parachutes complement the STFSI core computational technology in addressing these challenges. Until recently, these challenges were addressed for the Orion spacecraft main parachutes, which are the parachutes used for landing, and in the incompressible-flow regime, which is where the main parachutes operate. At higher altitudes the Orion spacecraft will rely on drogue parachutes. These parachutes have a ribbon construction, and in FSI modeling this creates geometric and flow complexities comparable to those encountered in FSI modeling of the main parachutes, which have a ringsail construction. Like the main parachutes, the drogue parachutes will be used in multiple stages-two reefed stages and a fully-open stage. A reefed stage is where a cable along the parachute skirt constrains the diameter to be less than the diameter in the subsequent stage. After a period of time during the descent at the reefed stage, the cable is cut and the parachute disreefs (i.e. expands) to the next stage. The reefed stages and disreefing involve computational challenges beyond those in FSI modeling of fully-open drogue parachutes. We present the special modeling techniques we devised to address the computational challenges and the results from the computations carried out. The flight envelope of the Orion drogue parachutes includes regions where the Mach number is high enough to require a compressible-flow solver. We present a preliminary fluid mechanics computation for such a case.

There are now some sophisticated and powerful methods for computer modeling of parachutes. These methods are capable of addressing some of the most formidable computational challenges encountered in parachute modeling, including fluid-structure interaction (FSI) between the parachute and air flow, design complexities such as those seen in spacecraft parachutes, and operational complexities such as use in clusters and disreefing. One should be able to extract from a reliable full-scale parachute modeling any data or analysis needed. In some cases, however, the parachute engineers may want to perform quickly an extended or repetitive analysis with methods based on simplified models. Some of the data needed by a simplified model can very effectively be extracted from a full-scale computer modeling that serves as a pilot. A good example of such data is the circumferential curvature of a parachute gore, where a gore is the slice of the parachute canopy between two radial reinforcement cables running from the parachute vent to the skirt. We present the multiscale methods we devised for gore curvature calculation from FSI modeling of spacecraft parachutes. The methods include those based on the multiscale sequentially-coupled FSI technique and using NURBS meshes. We show how the methods work for the fully-open and two reefed stages of the Orion spacecraft main and drogue parachutes.

Flow problems with moving boundaries and interfaces include fluid-structure interaction (FSI) and a number of other classes of problems, have an important place in engineering analysis and design, and offer some formidable computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian-Eulerian method (ALE-VMS). Since their inception, these two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid-object and fluid-particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid-object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the FSI modeling were increased with the special ALE-VMS and ST FSI techniques targeting each of those classes of problems. This article provides an overview of the core ALE-VMS and ST FSI techniques, their recent versions, and the special ALE-VMS and ST FSI techniques. It also provides examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.

We provide an overview of the aerodynamic and FSI analysis of wind turbines the first three authors' teams carried out in recent years with the ALE-VMS and ST-VMS methods. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian-Eulerian (ALE) method. The VMS components are from the residual-based VMS (RBVMS) method. The ST-VMS method is the VMS version of the deforming-spatial-domain/stabilized space-time (DSD/SST) method. The techniques complementing these core methods include weak enforcement of the essential boundary conditions, NURBS-based isogeometric analysis, using NURBS basis functions in temporal representation of the rotor motion, mesh motion and also in remeshing, rotation representation with constant angular velocity, Kirchhoff-Love shell modeling of the rotor-blade structure, and full FSI coupling. The analysis cases include the aerodynamics of standalone wind-turbine rotors, wind-turbine rotor and tower, and the FSI that accounts for the deformation of the rotor blades. The specific wind turbines considered are NREL 5MW, NREL Phase VI and Micon 65/13M, all at full scale, and our analysis for NREL Phase VI and Micon 65/13M includes comparison with the experimental data.

This paper provides a review of the space-time (ST) and Arbitrary Lagrangian-Eulerian (ALE) techniques developed by the first three authors' research teams for patient-specific cardiovascular fluid mechanics modeling, including fluid-structure interaction (FSI). The core methods are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized ST formulation, and the stabilized ST FSI technique. A good number of special techniques targeting cardiovascular fluid mechanics have been developed to be used with the core methods. These include: (i) arterial-surface extraction and boundary condition techniques, (ii) techniques for using variable arterial wall thickness, (iii) methods for calculating an estimated zero-pressure arterial geometry, (iv) techniques for prestressing of the blood vessel wall, (v) mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, (vi) a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, (vii) a scaling technique for specifying a more realistic volumetric flow rate, (viii) techniques for the projection of fluid-structure interface stresses, (ix) a recipe for pre-FSI computations that improve the convergence of the FSI computations, (x) the Sequentially-Coupled Arterial FSI technique and its multiscale versions, (xi) techniques for calculation of the wall shear stress (WSS) and oscillatory shear index (OSI), (xii) methods for stent modeling and mesh generation, (xiii) methods for calculation of the particle residence time, and (xiv) methods for an estimated element-based zero-stress state for the artery. Here we provide an overview of the special techniques for WSS and OSI calculations, stent modeling and mesh generation, and calculation of the residence time with application to pulsatile ventricular assist device (PVAD). We provide references for some of the other special techniques. With results from earlier computations, we show how these core and special techniques work.

Orion spacecraft main and drogue parachutes are used in multiple stages, starting with a "reefed" stage where a cable along the parachute skirt constrains the diameter to be less than the diameter in the subsequent stage. After a period of time during the descent, the cable is cut and the parachute "disreefs" (i.e. expands) to the next stage. Fluid-structure interaction (FSI) modeling of the reefed stages and disreefing involve computational challenges beyond those in FSI modeling of fully-open spacecraft parachutes. These additional challenges are created by the increased geometric complexities and by the rapid changes in the parachute geometry during disreefing. The computational challenges are further increased because of the added geometric porosity of the latest design of the Orion spacecraft main parachutes. The "windows" created by the removal of panels compound the geometric and flow complexity. That is because the Homogenized Modeling of Geometric Porosity, introduced to deal with the flow through the hundreds of gaps and slits involved in the construction of spacecraft parachutes, cannot accurately model the flow through the windows, which needs to be actually resolved during the FSI computation. In parachute FSI computations, the resolved geometric porosity is significantly more challenging than the modeled geometric porosity, especially in computing the reefed stages and disreefing. Orion spacecraft main and drogue parachutes will both have three stages, with computation of the Stage 1 shape and disreefing from Stage 1 to Stage 2 for the main parachute being the most challenging because of the lowest "reefing ratio" (the ratio of the reefed skirt diameter to the nominal diameter). We present the special modeling techniques and strategies we devised to address the computational challenges encountered in FSI modeling of the reefed stages and disreefing of the main and drogue parachutes. We report, for a single parachute, FSI computation of both reefed stages and both disreefing events for both the main and drogue parachutes. In the case of the main parachute, we also report, for a 2-parachute cluster, FSI computation of the disreefing from Stage 2 to Stage 3. With results from these computations, we demonstrate that we have to a great extent overcome one of the most formidable challenges in FSI modeling of spacecraft parachutes.

We present a computational method for simulation of particle-laden flows in turbomachinery. The method is based on a stabilized finite element fluid mechanics formulation and a finite element particle-cloud tracking method. We focus on induced-draft fans used in process industries to extract exhaust gases in the form of a two-phase fluid with a dispersed solid phase. The particle-laden flow causes material wear on the fan blades, degrading their aerodynamic performance, and therefore accurate simulation of the flow would be essential in reliable computational turbomachinery analysis and design. The turbulent-flow nature of the problem is dealt with a Reynolds-Averaged Navier-Stokes model and Streamline-Upwind/Petrov-Galerkin/Pressure-Stabilizing/Petrov-Galerkin stabilization, the particle-cloud trajectories are calculated based on the flow field and closure models for the turbulence-particle interaction, and one-way dependence is assumed between the flow field and particle dynamics. We propose a closure model utilizing the scale separation feature of the variational multiscale method, and compare that to the closure utilizing the eddy viscosity model. We present computations for axial- and centrifugal-fan configurations, and compare the computed data to those obtained from experiments, analytical approaches, and other computational methods.

To address the computational challenges associated with contact between moving interfaces, such as those in cardiovascular fluid-structure interaction (FSI), parachute FSI, and flapping-wing aerodynamics, we introduce a space-time (ST) interface-tracking method that can deal with topology change (TC). In cardiovascular FSI, our primary target is heart valves. The method is a new version of the deforming-spatial-domain/stabilized space-time (DSD/SST) method, and we call it ST-TC. It includes a master-slave system that maintains the connectivity of the "parent" mesh when there is contact between the moving interfaces. It is an efficient, practical alternative to using unstructured ST meshes, but without giving up on the accurate representation of the interface or consistent representation of the interface motion. We explain the method with conceptual examples and present 2D test computations with models representative of the classes of problems we are targeting.

Fluid mechanics computation of heart valves with an interface-tracking (moving-mesh) method was one of the classes of computations targeted in introducing the space-time (ST) interface tracking method with topology change (ST-TC). The ST-TC method is a new version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method. It can deal with an actual contact between solid surfaces in flow problems with moving interfaces, while still possessing the desirable features of interface-tracking methods, such as better resolution of the boundary layers. The DSD/SST method with effective mesh update can already handle moving-interface problems when the solid surfaces are in near contact or create near TC, if the "nearness" is sufficiently "near" for the purpose of solving the problem. That, however, is not the case in fluid mechanics of heart valves, as the solid surfaces need to be brought into an actual contact when the flow has to be completely blocked. Here we extend the ST-TC method to 3D fluid mechanics computation of heart valve models. We present computations for two models: an aortic valve with coronary arteries and a mechanical aortic valve. These computations demonstrate that the ST-TC method can bring interface-tracking accuracy to fluid mechanics of heart valves, and can do that with computational practicality.

We present a fluid-structure interaction (FSI) analysis of the blood flow and geometrical characteristics in the thoracic aorta. The FSI is handled with the sequentially-coupled arterial FSI technique. The fluid mechanics equations are solved with the ST-VMS method, which is the variational multiscale version of the deforming-spatial-domain/stabilized space-time (DSD/SST) method. We focus on the relationship between the centerline geometry of the aorta and the flow field, which influences the wall shear stress distribution. The centerlines of the aorta models we use in our analysis are extracted from the CT scans, and we assume a constant diameter. Torsion-free model geometries are generated by projecting the original centerline to its averaged plane of curvature. The flow fields for the original and projected geometries are compared to examine the influence of the torsion.

In patient-specific arterial fluid-structure interaction (FSI) computations the image-based arterial geometry comes from a configuration that is not stress-free. We present a method for estimation of element-based zero-stress (ZS) state. The method has three main components. (1) An iterative method, which starts with an initial guess for the ZS state, is used for computing the element-based ZS state such that when a given pressure load is applied, the image-based target shape is matched. (2) A method for straight-tube geometries with single and multiple layers is used for computing the element-based ZS state so that we match the given diameter and longitudinal stretch in the target configuration and the "opening angle." (3) An element-based mapping between the arterial and straight-tube configurations is used for mapping from the arterial configuration to the straight-tube configuration, and for mapping the estimated ZS state of the straight tube back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. We present a set of test computations to show how the method works.

We propose a method for coronary arterial dynamics computation with medical-image-based time-dependent anatomical models. The objective is to improve the computational analysis of coronary arteries for better understanding of the links between the atherosclerosis development and mechanical stimuli such as endothelial wall shear stress and structural stress in the arterial wall. The method has two components. The first one is element-based zero-stress (ZS) state estimation, which is an alternative to prestress calculation. The second one is a "mixed ZS state" approach, where the ZS states for different elements in the structural mechanics mesh are estimated with reference configurations based on medical images coming from different instants within the cardiac cycle. We demonstrate the robustness of the method in a patient-specific coronary arterial dynamics computation where the motion of a thin strip along the arterial surface and two cut surfaces at the arterial ends is specified to match the motion extracted from the medical images.

We present a sequentially-coupled space-time (ST) computational fluid-structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV). The wing motion and deformation data, whether prescribed fully or partially, is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The core computational FSI technology is based on the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) formulation. This is supplemented with using NURBS basis functions in temporal representation of the wing and mesh motion, and in remeshing. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called "DSD/SST-VMST." The structural mechanics computations are based on the Kirchhoff-Love shell model. The sequential-coupling technique is applicable to some classes of FSI problems, especially those with temporally-periodic behavior. We show that it performs well in FSI computations of the flapping-wing aerodynamics we consider here. In addition to the straight-flight case, we analyze cases where the MAV body has rolling, pitching, or rolling and pitching motion. We study how all these influence the lift and thrust.

This is an overview of the new directions we have taken the space-time (ST) methods in bringing solution and analysis to different classes of computationally challenging engineering problems. The classes of problems we have focused on include bio-inspired flapping-wing aerodynamics, wind-turbine aerodynamics, and cardiovascular fluid mechanics. The new directions for the ST methods include the variational multiscale version of the Deforming-Spatial-Domain/Stabilized ST method, using NURBS basis functions in temporal representation of the unknown variables and motion of the solid surfaces and fluid meshes, ST techniques with continuous representation in time, and ST interface-tracking with topology change. We describe the new directions and present examples of the challenging problems solved.

Flow in a sewage pump might carry many unpredictable solid objects. To understand better<br>how an object might wrap around the blades, we investigate the mechanism in a laboratory&nbsp;<br>model. The model consists of a cable and rigid obstacles. In the interaction between&nbsp;<br>the two, the friction forces play an important role because of the high friction coefficient&nbsp;<br>and the wrapping. To model this contact, we study it experimentally, measure the model&nbsp;<br>parameters, and test the model numerically.

We introduce space-time computation techniques with continuous representation in time (ST-C), using temporal NURBS basis functions. This gives us a temporally smooth, NURBS-based solution, which is desirable in some cases, and a more efficient way of dealing with the computed data. We propose two versions of ST-C. In the first version, the smooth solution is extracted by projection from a solution computed with a different temporal representation, typically a discontinuous one. We use a successive projection technique with a small number of temporal NURBS basis functions at each projection, and therefore the extraction can take place as the solution with discontinuous temporal representation is being computed, without storing a large amount of time-history data. This version is not limited to solutions computed with ST techniques. In the second version, the solution with continuous temporal representation is computed directly by using a small number of temporal NURBS basis functions in the variational formulation associated with each time step.

We present the space-time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

This paper provides a review of the space-time (ST) and Arbitrary Lagrangian-Eulerian (ALE) techniques developed by the first three authors' research teams for patient-specific cardiovascular fluid mechanics modeling, including fluid-structure interaction (FSI). The core methods are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized ST formulation, and the stabilized ST FSI technique. A good number of special techniques targeting cardiovascular fluid mechanics have been developed to be used with the core methods. These include: (i) arterial-surface extraction and boundary condition techniques, (ii) techniques for using variable arterial wall thickness, (iii) methods for calculating an estimated zero-pressure arterial geometry, (iv) techniques for prestressing of the blood vessel wall, (v) mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, (vi) a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, (vii) a scaling technique for specifying a more realistic volumetric flow rate, (viii) techniques for the projection of fluid-structure interface stresses, (ix) a recipe for pre-FSI computations that improve the convergence of the FSI computations, (x) the Sequentially-Coupled Arterial FSI technique and its multiscale versions, (xi) techniques for calculation of the wall shear stress (WSS) and oscillatory shear index (OSI), (xii) methods for stent modeling and mesh generation, (xiii) methods for calculation of the particle residence time, and (xiv) methods for an estimated element-based zero-stress state for the artery. Here we provide an overview of the special techniques for WSS and OSI calculations, stent modeling and mesh generation, and calculation of the residence time with application to pulsatile ventricular assist device (PVAD). We provide references for some of the other special techniques. With results from earlier computations, we show how these core and special techniques work. © 2014 World Scientific Publishing Company.

This chapter provides an overview of how patient-specific cardiovascular fluid mechanics analysis, including fluid-structure interaction (FSI), can be carried out with the space-time (ST) and Arbitrary Lagrangian-Eulerian (ALE) techniques developed by the first three authors' research teams. The core methods are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized ST formulation, and the stabilized ST FSI technique. A good number of special techniques targeting cardiovascular fluid mechanics have been developed to be used with the coremethods. These include (i) arterial-surface extraction and boundary condition techniques, (ii) techniques for using variable arterialwall thickness, (iii) methods for calculating an estimated zero-pressure arterial geometry, (iv) techniques for prestressing of the blood vessel wall, (v) mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, (vi) a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, (vii) a scaling technique for specifying a more realistic volumetric flow rate, (viii) techniques for the projection of fluid-structure interface stresses, (ix) a recipe for pre-FSI computations that improve the convergence of the FSI computations, (x) the Sequentially-Coupled Arterial FSI technique and its multiscale versions, (xi) techniques for calculation of the wall shear stress (WSS) and oscillatory shear index (OSI), (xii) methods for stent modeling and mesh generation, (xiii) methods for calculation of the particle residence time, and (xiv) methods for an estimated element-based zero-stress state for the artery. Here we provide an overview of the special techniques for stent modeling and mesh generation and calculation of the residence time with application to pulsatile ventricular assist device (PVAD). We provide references for some of the other special techniques. With results from earlier computations, we show how the core and special techniques work.

We provide an overview of the special techniques developed earlier by the Team for Advanced Flow Simulation and Modeling (TwAFSM) for fluid–structure interaction (FSI) modeling of patient-specific cerebral aneurysms. The core FSI techniques are the Deforming-Spatial-Domain/Stabilized Space– Time formulation and the stabilized space–time FSI technique. The special techniques include techniques for calculating an estimated zero-pressure arterial geometry, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, techniques for calculation of the wall shear stress and oscillatory shear index, and arterial-surface extraction and boundary condition techniques. We show, with results from earlier computations, how these techniques work. We also describe the arterial FSI techniques developed and implemented recently by the TwAFSM and present a sample from a wide set of patient-specific cerebral-aneurysm models we computed recently.

We provide an overview of the aerodynamic and FSI analysis of wind turbines the first three authors' teams carried out in recent years with the ALE-VMS and ST-VMS methods. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian-Eulerian (ALE) method. The VMS components are from the residual-based VMS (RBVMS) method. The ST-VMS method is the VMS version of the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) method. The techniques complementing these core methods include weak enforcement of the essential boundary conditions, NURBS-based isogeometric analysis, using NURBS basis functions in temporal representation of the rotor motion, mesh motion and also in remeshing, rotation representation with constant angular velocity, Kirchhoff-Love shell modeling of the rotor-blade structure, and full FSI coupling. The analysis cases include the aerodynamics of wind-turbine rotor and tower and the FSI that accounts for the deformation of the rotor blades. The specific wind turbines considered are NREL 5MW, NREL Phase VI and Micon 65/13M, all at full scale, and our analysis for NREL Phase VI and Micon 65/13M includes comparison with the experimental data.

Flows with moving interfaces include fluid-structure interaction (FSI) and quite a few other classes of problems, have an important place in engineering analysis and design, and pose significant computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian-Eulerian method (ALE-VMS). These two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid-object and fluid-particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid-object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the modeling were increased with the special ALE-VMS and ST techniques targeting each of those classes of problems. This article provides an overview of how the core and special ALE-VMS and ST techniques are used in computational engineering analysis and design. The article includes an overview of three of the special ALE-VMS and ST techniques, which are just a few examples of the many special techniques that complement the core methods. The impact of the ALE-VMS and ST methods in engineering analysis and design are shown with examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.

To increase aerodynamic performance, the geometric porosity of a ringsail spacecraft parachute canopy is sometimes increased, beyond the "rings" and "sails" with hundreds of "ring gaps" and "sail slits." This creates extra computational challenges for fluid-structure interaction (FSI) modeling of clusters of such parachutes, beyond those created by the lightness of the canopy structure, geometric complexities of hundreds of gaps and slits, and the contact between the parachutes of the cluster. In FSI computation of parachutes with such "modified geometric porosity," the flow through the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the Homogenized Modeling of Geometric Porosity (HMGP), which was introduced to deal with the hundreds of gaps and slits. The flow needs to be actually resolved. All these computational challenges need to be addressed simultaneously in FSI modeling of clusters of spacecraft parachutes with modified geometric porosity. The core numerical technology is the Stabilized Space-Time FSI (SSTFSI) technique, and the contact between the parachutes is handled with the Surface-Edge-Node Contact Tracking (SENCT) technique. In the computations reported here, in addition to the SSTFSI and SENCT techniques and HMGP, we use the special techniques we have developed for removing the numerical spinning component of the parachute motion and for restoring the mesh integrity without a remesh. We present results for 2- and 3-parachute clusters with two different payload models.

We present an overview of the special computer modeling techniques we have developed recently for flapping-wing aerodynamics of a locust. The wing motion and deformation data is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The special techniques have been developed around our core computational technique, which is the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called "DSD/SST-VMST." The special techniques are based on using, in the space-time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the locust wings. Temporal NURBS basis functions are used also in representation of the motion of the volume meshes computed and in remeshing. In this special-issue paper, we present a condensed version of the material from [1], concentrating on the flapping-motion modeling and computations, and also a temporal-order study from [2]. (C) 2012 Elsevier Ltd. All rights reserved.

We present a patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. The analysis is based on four different arterial models extracted form medical images, and the stent is placed across the neck of the aneurysm to reduce the flow circulation in the aneurysm. The core computational technique used in the analysis is the space-time (ST) version of the variational multiscale (VMS) method and is called "DSD/SST-VMST". The special techniques developed for this class of cardiovascular fluid mechanics computations are used in conjunction with the DSD/SST-VMST technique. The special techniques include NURBS representation of the surface over which the stent model and mesh are built, mesh generation with a reasonable resolution across the width of the stent wire and with refined layers of mesh near the arterial and stent surfaces, modeling the double-stent case, and quantitative assessment of the flow circulation in the aneurysm. We provide a brief overview of the special techniques, compute the unsteady flow patterns in the aneurysm for the four arterial models, and investigate in each case how those patterns are influenced by the presence of single and double stents.

We present patient-specific computational fluid mechanics analysis of blood flow in cerebral arteries with aneurysm and stent. The special arterial fluid mechanics techniques we have developed for this are used in conjunction with the core computational technique, which is the space-time version of the variational multiscale (VMS) method and is called "DST/SST-VMST." The special techniques include using a nonuniform rational basis spline for the spatial representation of the surface over which the stent mesh is built, mesh generation techniques for both the finite- and zero-thickness representations of the stent, techniques for generating refined layers of mesh near the arterial and stent surfaces, and models for representing double stents. We compute the unsteady flow patterns in the aneurysm and investigate how those patterns are influenced by the presence of single and double stents. We also compare the flow patterns obtained with the finite- and zero-thickness representations of the stent. This edition first published 2013 © 2013 John Wiley &amp
Sons, Ltd.

Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation was developed for flow problems with moving interfaces and has been successfully applied to some of the most complex problems in that category. A new version of the DSD/SST method for incompressible flows, which has additional subgrid-scale representation features, is the space-time version of the residual-based variational multiscale (VMS) method. This new version, called DSD/SST-VMST and also Space-Time VMS (ST-VMS), provides a more comprehensive framework for the VMS method. We describe the ST-VMS method, including the embedded stabilization parameters, and assess its performance in computation of flow problems at high Reynolds numbers by comparing the results to experimental data. The computations, which include those with 3D airfoil geometries and spacecraft configurations, signal a promising future for the ST-VMS method. © 2013 World Scientific Publishing Company.

Fluid-structure interaction (FSI) modeling of spacecraft parachutes involves a number of computational challenges beyond those encountered in a typical FSI problem. The stabilized space-time FSI (SSTFSI) technique serves as a robust and accurate core FSI method, and a number of special FSI methods address the computational challenges specific to spacecraft parachutes. Some spacecraft FSI problems involve even more specific computational challenges and require additional special methods. An example of that is the impulse ejection and parachute extraction of a protective cover used in a spacecraft. The computational challenges specific to this problem are related to the sudden changes in the parachute loads and sudden separation of the cover with very little initial clearance from the spacecraft. We describe the core and special FSI methods, and present the methods we use in FSI analysis of the parachute dynamics and cover separation, including the temporal NURBS representation in modeling the separation motion.

In this lead paper of the special issue, we provide some comments on challenges and directions in computational fluid-structure interaction (FSI). We briefly discuss the significance of computational FSI methods, their components, moving-mesh and nonmoving-mesh methods, mesh moving and remeshing concepts, and FSI coupling techniques. © 2013 World Scientific Publishing Company.

Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation was developed for flow problems with moving interfaces and has been successfully applied to some of the most complex problems in that category. A new version of the DSD/SST method for incompressible flows, which has additional subgrid-scale representation features, is the space-time version of the residual-based variational multiscale (VMS) method. This new version, called DSD/SST-VMST and also Space-Time VMS (ST-VMS), provides a more comprehensive framework for the VMS method. We describe the ST-VMS method, including the embedded stabilization parameters, and assess its performance in computation of flow problems at high Reynolds numbers by comparing the results to experimental data. The computations, which include those with 3D airfoil geometries and spacecraft configurations, signal a promising future for the ST-VMS method.

Fluid-structure interaction (FSI) modeling of spacecraft parachutes involves a number of computational challenges beyond those encountered in a typical FSI problem. The stabilized space-time FSI (SSTFSI) technique serves as a robust and accurate core FSI method, and a number of special FSI methods address the computational challenges specific to spacecraft parachutes. Some spacecraft FSI problems involve even more specific computational challenges and require additional special methods. An example of that is the impulse ejection and parachute extraction of a protective cover used in a spacecraft. The computational challenges specific to this problem are related to the sudden changes in the parachute loads and sudden separation of the cover with very little initial clearance from the spacecraft. We describe the core and special FSI methods, and present the methods we use in FSI analysis of the parachute dynamics and cover separation, including the temporal NURBS representation in modeling the separation motion. © 2013 World Scientific Publishing Company.

In this lead paper of the special issue, we provide some comments on challenges and directions in computational fluid-structure interaction (FSI). We briefly discuss the significance of computational FSI methods, their components, moving-mesh and nonmoving-mesh methods, mesh moving and remeshing concepts, and FSI coupling techniques.

Computational Fluid-Structure Interaction: Methods and Applications takes the reader from the fundamentals of computational fluid and solid mechanics to the state-of-the-art in computational FSI methods, special FSI techniques, and solution of real-world problems. Leading experts in the field present the material using a unique approach that combines advanced methods, special techniques, and challenging applications. This book begins with the differential equations governing the fluid and solid mechanics, coupling conditions at the fluid-solid interface, and the basics of the finite element method. It continues with the ALE and space-time FSI methods, spatial discretization and time integration strategies for the coupled FSI equations, solution techniques for the fully-discretized coupled equations, and advanced FSI and space-time methods. It ends with special FSI techniques targeting cardiovascular FSI, parachute FSI, and wind-turbine aerodynamics and FSI. Key features: First book to address the state-of-the-art in computational FSI Combines the fundamentals of computational fluid and solid mechanics, the state-of-the-art in FSI methods, and special FSI techniques targeting challenging classes of real-world problems Covers modern computational mechanics techniques, including stabilized, variational multiscale, and space-time methods, isogeometric analysis, and advanced FSI coupling methods. Is in full color, with diagrams illustrating the fundamental concepts and advanced methods and with insightful visualization illustrating the complexities of the problems that can be solved with the FSI methods covered in the book. Authors are award winning, leading global experts in computational FSI, who are known for solving some of the most challenging FSI problems. Computational Fluid-Structure Interaction: Methods and Applications is a comprehensive reference for researchers and practicing engineers who would like to advance their existing knowledge on these subjects. It is also an ideal text for graduate and senior-level undergraduate courses in computational fluid mechanics and computational FSI. © 2013 John Wiley &amp
Sons, Ltd.

We present the special space-time computational techniques we have introduced recently for computational aerodynamics modeling of flapping wings of an actual locust. These techniques have been designed to be used with the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, which is the core computational technique. The DSD/SST formulation was developed for flow problems with moving interfaces and was elevated to newer versions over the years, including the space-time version of the residual-based variational multiscale (VMS) method, which is called "DSD/SST-VMST" and used in the computations reported here. The special space-time techniques are based on using, in the space-time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the locust wings. The motion and deformation data is extracted from the high-speed, multi-camera video recordings of a locust in a wind tunnel. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. These ingredients provide an accurate and efficient way of dealing with the wind tunnel data and the mesh. The computations demonstrate the effectiveness of the core and special space-time techniques in modeling the aerodynamics of flapping wings, with the wing motion and deformation coming from an actual locust.

We present a detailed computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle (MAV). The computational techniques used include the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, which serves as the core computational technique. The DSD/SST formulation is a moving-mesh technique, and in the computations reported here we use the space-time version of the residual-based variational multiscale (VMS) method, which is called "DSD/SST-VMST." The motion and deformation of the wings are based on data extracted from the high-speed, multi-camera video recordings of a locust in a wind tunnel. A set of special space-time techniques are also used in the computations in conjunction with the DSD/SST method. The special techniques are based on using, in the space-time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the wings and for the mesh moving and remeshing. The computational analysis starts with the computation of the base case, and includes computations with increased temporal and spatial resolutions compared to the base case. In increasing the temporal resolution, we separately test increasing the temporal order, the number of temporal subdivisions, and the frequency of remeshing. In terms of the spatial resolution, we separately test increasing the wing-mesh refinement in the normal and tangential directions and changing the way node connectivities are handled at the wingtips. The computational analysis also includes using different combinations of wing configurations for the MAV and investigating the beneficial and disruptive interactions between the wings and the role of wing camber and twist.

We present the special arterial fluid mechanics techniques we have developed for patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. These techniques are used in conjunction with the core computational technique, which is the space-time version of the variational multiscale (VMS) method and is called "DST/SST-VMST." The special techniques include using NURBS for the spatial representation of the surface over which the stent mesh is built, mesh generation techniques for both the finite-and zero-thickness representations of the stent, techniques for generating refined layers of mesh near the arterial and stent surfaces, and models for representing double stent. We compute the unsteady flow patterns in the aneurysm and investigate how those patterns are influenced by the presence of single and double stents. We also compare the flow patterns obtained with the finite- and zero-thickness representations of the stent.

Fluid-structure interaction (FSI) modeling of parachutes poses a number of computational challenges. These include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of ringsail parachutes the geometric porosity created by the construction of the canopy from "rings" and "sails" with hundreds of "ring gaps" and "sail slits," in the case of parachute clusters the contact between the parachutes, and "disreefing" from one stage to another when the parachute is used in multiple stages. The Team for Advanced Flow Simulation and Modeling (T*AFSM) has been successfully addressing these computational challenges with the Stabilized Space-Time FSI (SSTFSI) technique, which was developed and improved over the years by the T*AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the T*AFSM, which are applicable to cases with nonmatching fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light. The special technique used in dealing with the geometric complexities of the rings and sails is the homogenized modeling of geometric porosity (HMGP), which was developed and improved in recent years by the T*AFSM. The surface-edge-node contact tracking (SENCT) technique was introduced by the T*AFSM as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the T*AFSM. As an additional computational challenge, the parachute canopy might, by design, have some of its panels and sails removed. In FSI computation of parachutes with such "modified geometric porosity," the flowthrough the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the HMGP and needs to be actually resolved during the FSI computation. In this paper we focus on parachute disreefing, including the disreefing of parachute clusters, and parachutes with modified geometric porosity, including the reefed stages of such parachutes. We describe the additional special techniques we have developed to address the challenges involved and report FSI computations for parachutes and parachute clusters with disreefing and modified geometric porosity.

Since its introduction in 1991 for computation of flow problems with moving boundaries and interfaces, the Deforming-Spatial-Domain/Stabilized SpaceTime (DSD/SST) formulation has been applied to a diverse set of challenging problems. The classes of problems computed include free-surface and two-fluid flows, fluidobject, fluidparticle and fluidstructure interaction (FSI), and flows with mechanical components in fast, linear or rotational relative motion. The DSD/SST formulation, as a core technology, is being used for some of the most challenging FSI problems, including parachute modeling and arterial FSI. Versions of the DSD/SST formulation introduced in recent years serve as lower-cost alternatives. More recent variational multiscale (VMS) version, which is called DSD/SST-VMST (and also ST-VMS), has brought better computational accuracy and serves as a reliable turbulence model. Special spacetime FSI techniques introduced for specific classes of problems, such as parachute modeling and arterial FSI, have increased the scope and accuracy of the FSI modeling in those classes of computations. This paper provides an overview of the core spacetime FSI technique, its recent versions, and the special spacetime FSI techniques. The paper includes test computations with the DSD/SST-VMST technique. © 2012 World Scientific Publishing Company.

We provide an overview of the Arbitrary LagrangianEulerian Variational Multiscale (ALE-VMS) and SpaceTime Variational Multiscale (ST-VMS) methods we have developed for computer modeling of wind-turbine rotor aerodynamics and fluidstructure interaction (FSI). The related techniques described include weak enforcement of the essential boundary conditions, KirchhoffLove shell modeling of the rotor-blade structure, NURBS-based isogeometric analysis, and full FSI coupling. We present results from application of these methods to computer modeling of NREL 5MW and NREL Phase VI wind-turbine rotors at full scale, including comparison with experimental data. © 2012 World Scientific Publishing Company.

Since its introduction in 1991 for computation of flow problems with moving boundaries and interfaces, the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation has been applied to a diverse set of challenging problems. The classes of problems computed include free-surface and two-fluid flows, fluid-object, fluid-particle and fluid-structure interaction (FSI), and flows with mechanical components in fast, linear or rotational relative motion. The DSD/SST formulation, as a core technology, is being used for some of the most challenging FSI problems, including parachute modeling and arterial FSI. Versions of the DSD/SST formulation introduced in recent years serve as lower-cost alternatives. More recent variational multiscale (VMS) version, which is called DSD/SST-VMST (and also ST-VMS), has brought better computational accuracy and serves as a reliable turbulence model. Special space-time FSI techniques introduced for specific classes of problems, such as parachute modeling and arterial FSI, have increased the scope and accuracy of the FSI modeling in those classes of computations. This paper provides an overview of the core space-time FSI technique, its recent versions, and the special space-time FSI techniques. The paper includes test computations with the DSD/SST-VMST technique.

We provide an overview of the Arbitrary Lagrangian-Eulerian Variational Multiscale (ALE-VMS) and Space-Time Variational Multiscale (ST-VMS) methods we have developed for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction (FSI). The related techniques described include weak enforcement of the essential boundary conditions, Kirchhoff-Love shell modeling of the rotor-blade structure, NURBS-based isogeometric analysis, and full FSI coupling. We present results from application of these methods to computer modeling of NREL 5MW and NREL Phase VI wind-turbine rotors at full scale, including comparison with experimental data.

This is an extensive overview of the core and special space-time and Arbitrary Lagrangian-Eulerian (ALE) techniques developed by the authors' research teams for patient-specific cardiovascular fluid-structure interaction (FSI) modeling. The core techniques are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized Space-Time formulation, and the stabilized space-time FSI technique. The special techniques include methods for calculating an estimated zero-pressure arterial geometry, prestressing of the blood vessel wall, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, the Sequentially-Coupled Arterial FSI technique and its multiscale versions, techniques for the projection of fluid-structure interface stresses, calculation of the wall shear stress and oscillatory shear index, arterial-surface extraction and boundary condition techniques, and a scaling technique for specifying a more realistic volumetric flow rate. With results from earlier computations, we show how these core and special FSI techniques work in patient-specific cardiovascular simulations.

The computational challenges posed by fluid-structure interaction (FSI) modeling of parachutes include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of "ringsail" parachutes the geometric complexities created by the construction of the canopy from "rings" and "sails" with hundreds of ring "gaps" and sail "slits", and in the case of parachute clusters the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T*AFSM) has successfully addressed these computational challenges with the Stabilized Space-Time FSI (SSTFSI) technique, which was developed and improved over the years by the T*AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the T * AFSM, which are applicable to cases with incompatible fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light and therefore more sensitive to the variations in the fluid dynamics forces. The special technique used in dealing with the geometric complexities of the rings and sails is the Homogenized Modeling of Geometric Porosity, which was developed and improved in recent years by the T*AFSM. The Surface-Edge-Node Contact Tracking (SENCT) technique was introduced by the T*AFSM as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the T*AFSM. We provide an overview of the core and special techniques developed by the T*AFSM, present single-parachute FSI computations carried out for design-parameter studies, and report FSI computation and dynamical analysis of two-parachute clusters.

We present the special space-time computational techniques we have introduced recently for computation of flow problems with moving and deforming solid surfaces. The techniques have been designed in the context of the deforming-spatial-domain/stabilized space-time formulation, which was developed by the Team for Advanced Flow Simulation and Modeling for computation of flow problems with moving boundaries and interfaces. The special space-time techniques are based on using, in the space-time flow computations, non-uniform rational B-splines (NURBS) basis functions for the temporal representation of the motion and deformation of the solid surfaces and also for the motion and deformation of the volume meshes computed. This provides a better temporal representation of the solid surfaces and a more effective way of handling the volume-mesh motion. We apply these techniques to computation of the aerodynamics of flapping wings, specifically locust wings, where the prescribed motion and deformation of the wings are based on digital data extracted from the videos of the locust in a wind tunnel. We report results from the preliminary computations. [DOI: 10.1115/1.4005073]

Even though computer modeling of spacecraft parachutes involves a number of numerical challenges, advanced techniques developed in recent years for fluid-structure interaction (FSI) modeling in general and for parachute FSI modeling specifically have made simulation-based design studies possible. In this paper we focus on such studies for a single main parachute to be used with the Orion spacecraft. Although these large parachutes are typically used in clusters of two or three parachutes, studies for a single parachute can still provide valuable information for performance analysis and design and can be rather extensive. The major challenges in computer modeling of a single spacecraft parachute are the FSI between the air and the parachute canopy and the geometric complexities created by the construction of the parachute from "rings" and "sails" with hundreds of gaps and slits. The Team for Advanced Flow Simulation and Modeling has successfully addressed the computational challenges related to the FSI and geometric complexities, and has also been devising special procedures as needed for specific design parameter studies. In this paper we present parametric studies based on the suspension line length, canopy loading, and the length of the overinflation control line. [DOI: 10.1115/1.4005070]

We present an extensive comparative study based on patient-specific fluid-structure interaction (FSI) modeling of cerebral aneurysms. We consider a total of ten cases, at three different locations, half of which ruptured. We use the stabilized space-time FSI technique developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM), together with a number of special techniques targeting arterial FSI modeling, which were also developed by the T*AFSM. What we look at in our comparisons includes the wall shear stress, oscillatory shear index and the arterial-wall stress and stretch. We also investigate how simpler approaches to computer modeling of cerebral aneurysms perform compared to FSI modeling. [DOI: 10.1115/1.4005071]

We present our numerical-performance studies for 3D wind-turbine rotor aerodynamics computation with the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. As the test case, we use the NREL 5MW offshore baseline wind-turbine rotor. We compute the problem with both the original version of the DSD/SST formulation and the version with an advanced turbulence model. The DSD/SST formulation with the turbulence model is a recently-introduced space-time version of the residual-based variational multiscale method. We include in our comparison as reference solution the results obtained with the residual-based variational multiscale Arbitrary Lagrangian-Eulerian method using NURBS for spatial discretization. We test different levels of mesh refinement and different definitions for the stabilization parameter embedded in the "least squares on incompressibility constraint" stabilization. We compare the torque values obtained.

We provide an extensive overview of the core and special techniques developed earlier by the Team for Advanced Flow Simulation and Modeling (T star AFSM) for space-time fluid-structure interaction (FSI) modeling of patient-specific cerebral aneurysms. The core FSI techniques are the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation and the stabilized space-time FSI (SSTFSI) technique. The special techniques include techniques for calculating an estimated zero-pressure (EZP) arterial geometry, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, the Sequentially-Coupled Arterial FSI (SCAFSI) technique and its multiscale versions, techniques for the projection of fluid-structure interface stresses, calculation of the wall shear stress (WSS) and calculation of the oscillatory shear index (OSI) and arterial-surface extraction and boundary condition techniques. We show how these techniques work with results from earlier computations. We also describe the arterial FSI techniques developed and implemented recently by the T star AFSM and present a sample from a wide set of patient-specific cerebral-aneurysm models we computed recently. Copyright (C) 2011 John Wiley & Sons, Ltd.

We show how we use the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation for accurate 3D computation of the aerodynamics of a wind-turbine rotor. As the test case, we use the NREL 5MW offshore baseline wind-turbine rotor. This class of computational problems are rather challenging, because they involve large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. We compute the problem with both the original version of the DSD/SST formulation and a recently introduced version with an advanced turbulence model. The DSD/SST formulation with the advanced turbulence model is a space-time version of the residual-based variational multiscale method. We compare our results to those reported recently, which were obtained with the residual-based variational multiscale Arbitrary Lagrangian-Eulerian method using NURBS for spatial discretization and which we take as the reference solution. While the original DSD/SST formulation yields torque values not far from the reference solution, the DSD/SST formulation with the variational multiscale turbulence model yields torque values very close to the reference solution.

Computer modeling of spacecraft parachutes, which are quite often used in clusters of two or three large parachutes, involves fluid-structure interaction (FSI) between the parachute canopy and the air, geometric complexities created by the construction of the parachute from "rings" and "sails" with hundreds of gaps and slits, and the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T*AFSM) has successfully addressed the computational challenges related to the FSI and geometric complexities, and recently started addressing the challenges related to the contact between the parachutes of a cluster. The core numerical technology is the stabilized space-time FSI technique developed and improved over the years by the T*AFSM . The special technique used in dealing with the geometric complexities is the Homogenized Modeling of Geometric Porosity, which was also developed and improved in recent years by the T*AFSM . In this paper we describe the technique developed by the T*AFSM for modeling, in the context of an FSI problem, the contact between two structural surfaces. We show how we use this technique in dealing with the contact between parachutes. We present the results obtained with the FSI computation of parachute clusters, the related dynamical analysis, and a special decomposition technique for parachute descent speed to make that analysis more informative. We also present a special technique for extracting from a parachute FSI computation model parameters, such as added mass, that can be used in fast, approximate engineering analysis models for parachute dynamics.

We present the multiscale space-time techniques we have developed for fluid-structure interaction (FSI) computations. Some of these techniques are multiscale in the way the time integration is performed (i.e. temporally multiscale), some are multiscale in the way the spatial discretization is done (i.e. spatially multiscale), and some are in the context of the sequentially-coupled FSI (SCFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM). In the multiscale SCFSI technique, the FSI computational effort is reduced at the stage we do not need it and the accuracy of the fluid mechanics (or structural mechanics) computation is increased at the stage we need accurate, detailed flow (or structure) computation. As ways of increasing the computational accuracy when or where needed, and beyond just increasing the mesh refinement or decreasing the time-step size, we propose switching to more accurate versions of the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, using more polynomial power for the basis functions of the spatial discretization or time integration, and using an advanced turbulence model. Specifically, for more polynomial power in time integration, we propose to use NURBS, and as an advanced turbulence model to be used with the DSD/SST formulation, we introduce a space-time version of the residual-based variational multiscale method. We present a number of test computations showing the performance of the multiscale space-time techniques we are proposing. We also present a stability and accuracy analysis for the higher-accuracy versions of the DSD/SST formulation.

Iterative solution of large sparse nonsymmetric linear equation systems is one of the numerical challenges in arterial fluid-structure interaction computations. This is because the fluid mechanics parts of the fluid + structure block of the equation system that needs to be solved at every nonlinear iteration of each time step corresponds to incompressible flow, the computational domains include slender parts, and accurate wall shear stress calculations require boundary layer mesh refinement near the arterial walls. We propose a hybrid parallel sparse algorithm, domain-decomposing parallel solver (DDPS), to address this challenge. As the test case, we use a fluid mechanics equation system generated by starting with an arterial shape and flow field coming from an FSI computation and performing two time steps of fluid mechanics computation with a prescribed arterial shape change, also coming from the FSI computation. We show how the DDPS algorithm performs in solving the equation system and demonstrate the scalability of the algorithm.

The computational challenges posed by fluid-structure interaction (FSI) modeling of ringsail parachute clusters include the lightness of the membrane and cable structure of the canopy compared to the air masses involved in the parachute dynamics, geometric complexities created by the construction of the canopy from "rings" and "sails" with hundreds of ring gaps and sail slits, and the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T star AFSM) has successfully addressed these computational challenges with the Stabilized Space-Time FSI technique (SSTFSI), which was developed and improved over the years by the T star AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI. We present the results obtained with the FSI computation of parachute clusters and the related dynamical analysis.

Computer modeling of ringsail parachute clusters involves fluid structure interaction (FSI) between the parachute canopy and the air, geometric complexities created by the construction of the parachute from "rings" and "sails" with hundreds of gaps and slits, and the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T star AFSM) has successfully addressed the computational challenges related to the FSI and geometric complexities, and recently started addressing the challenges related to the contact between the parachutes of a cluster. This is being accomplished with the Stabilized Space-Time FSI technique, which was developed and improved over the years by the T star AFSM and serves as the core numerical technology, and the special techniques developed by the T star AFSM to deal with the geometric complexities and the contact between parachutes. We present the results obtained with the FSI computation of parachute clusters and the related dynamical analysis.

We address the computational challenges related to the extraction of the arterial-lumen geometry, mesh generation and starting-point determination in the computation of arterial fluid-structure interactions (FSI) with patient-specific data. The methods we propose here to address those challenges include techniques for constructing suitable cutting planes at the artery inlets and outlets and specifying on those planes proper boundary conditions for the fluid mechanics, structural mechanics and fluid mesh motion and a technique for the improved calculation of an estimated zero-pressure arterial geometry. We use the stabilized space-time FSI technique, together with a number of special techniques recently developed for arterial FSI. We focus on three patient-specific cerebral artery segments with aneurysm, where the lumen geometries are extracted from 3D rotational angiography. Copyright (C) 2010 John Wiley & Sons, Ltd.

Arterial fluid-structure interaction (FSI) computations involve a number of numerical challenges. Because blood flow is incompressible, iterative solution of the fluid mechanics part of the linear equation system at every nonlinear iteration of each time step is one of those challenges, especially for computations over slender domains and in the presence of boundary layer mesh refinement. In this paper we address that challenge. As test cases, we use equation systems from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm, with thin layers of elements near the arterial wall. We show how the preconditioning techniques, we propose for solving these large sparse nonsymmetric systems, perform at different time steps of the computation over a cardiac cycle. We also present a new hybrid parallel sparse linear system solver 'DD-Spike' and demonstrate its scalability. Copyright (C) 2010 John Wiley & Sons, Ltd.

A number of multiscale space time techniques have been developed recently by the Team for Advanced Flow Simulation and Modeling (T star AFSM) for fluid structure interaction computations. As part of that, we have introduced a space time version of the residual-based variational multiscale method. It has been designed in the context of the Deforming-Spatial-Domain/Stabilized Space Time formulation, which was developed earlier by the T star AFSM for computation of flow problems with moving boundaries and interfaces. We describe this multiscale space time technique, and present results from test computations.

We describe how the spatially multiscale Sequentially-Coupled Fluid-Structure Interaction (SCFSI) techniques we have developed, specifically the "SCFSI M2C", which is spatially multiscale for the structural mechanics part, can be used for increasing the accuracy of the membrane and cable structural mechanics solution in parachute FSI computations. The SCFSI M2C technique is used here in conjunction with the Stabilized Space-Time FSI (SSTFSI) technique, which was developed and improved over the years by the Team for Advanced Flow Simulation and Modeling (T star AFSM) and serves as the core numerical technology, and a number of special parachute FSI techniques developed by the T star AFSM in conjunction with the SSTFSI technique.

The team for advanced flow simulation and modeling (T star AFSM) has successfully addressed many of the computational challenges involved in fluid-structure interaction (FSI) modeling of ringsail parachutes, including the geometric complexities, and recently started addressing the challenges related to the contact between the parachutes of a cluster. This is being accomplished with the stabilized space-time FSI technique, which was developed by the T star AFSM and serves as the core numerical technology, and the special techniques developed by the T star AFSM. We present the results obtained with the FSI computation of parachute clusters and the related dynamical analysis.

We address some of the computational challenges involved in fluid-structure interaction (FSI) modeling of clusters of ringsail parachutes. The geometric complexity created by the construction of the parachute from 'rings' and 'sails' with hundreds of gaps and slits makes this class of FSI modeling inherently challenging. There is still much room for advancing the computational technology for FSI modeling of a single raingsail parachute, such as improving the Homogenized Modeling of Geometric Porosity (HMGP) and developing special techniques for computing the reefed stages of the parachute and its disreefing. While we continue working on that, we are also developing special techniques targeting cluster modeling, so that the computational technology goes beyond the single parachute and the challenges specific to parachute clusters are addressed. The rotational-periodicity technique we describe here is one of such special techniques, and we use that for computing good starting conditions for FSI modeling of parachute clusters. In addition to reporting our preliminary FSI computations for parachute clusters, we present results from those starting-condition computations. In the category of more fundamental computational technologies, we discuss how we are improving the HMGP by increasing the resolution of the fluid mechanics mesh used in the HMGP computation and also by increasing the number of gores used. Also in that category, we describe how we use the multiscale sequentially coupled FSI techniques to improve the accuracy in computing the structural stresses in parts of the structure where we want to report more accurate values. All these special techniques are used in conjunction with the Stabilized Space-Time Fluid-Structure Interaction (SSTFSI) technique. Therefore, we also present in this paper a brief stability and accuracy analysis for the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, which is the core numerical technology of the SSTFSI technique. Copyright (C) 2010 John Wiley & Sons, Ltd.

We focus on fluid-structure interaction (FSI) modeling and performance analysis of the ringsail parachutes to be used with the Orion spacecraft. We address the computational challenges with the latest techniques developed by the T star AFSM (Team for Advanced Flow Simulation and Modeling) in conjunction with the SSTFSI (Stabilized Space-Time Fluid-Structure Interaction) technique. The challenges involved in FSI modeling include the geometric porosity of the ringsail parachutes with ring gaps and sail slits. We investigate the performance of three possible design configurations of the parachute canopy. We also describe the techniques developed recently for building a consistent starting condition for the FSI computations, discuss rotational periodicity techniques for improving the geometric-porosity modeling, and introduce a new version of the HMGP (Homogenized Modeling of Geometric Porosity). Copyright (C) 2010 John Wiley & Sons, Ltd.

We consider a total of ten cases, at three different locations, half of which ruptured sometime after the images were taken. We use the stabilized space time FSI technique developed by the Team for Advanced Flow Simulation and Modeling, together with a number of special techniques targeting arterial FSI modeling. We compare the ten cases based on the wall shear stress, oscillatory shear index, and the arterial-wall stress. We also investigate how simpler approaches to computer modeling of cerebral aneurysms perform compared to FSI modeling.

In this two-part paper we present a collection of numerical methods combined into a single framework, which has the potential for a successful application to wind turbine rotor modeling and simulation. In Part 1 of this paper we focus on: 1. The basics of geometry modeling and analysis-suitable geometry construction for wind turbine rotors; 2. The fluid mechanics formulation and its suitability and accuracy for rotating turbulent flows; 3. The coupling of air flow and a rotating rigid body. In Part 2 we focus on the structural discretization for wind turbine blades and the details of the fluid-structure interaction computational procedures. The methods developed are applied to the simulation of the NREL 5MW offshore baseline wind turbine rotor. The simulations are performed at realistic wind velocity and rotor speed conditions and at full spatial scale. Validation against published data is presented and possibilities of the newly developed computational framework are illustrated on several examples. Copyright (C) 2010 John Wiley & Sons, Ltd.

New special fluid-structure interaction (FSI) techniques, supplementing the ones developed earlier, are employed with the Stabilized Space-Time FSI (SSTFSI) technique. The new special techniques include improved ways of calculating the equivalent fabric porosity in Homogenized Modeling of Geometric Porosity (HMGP), improved ways of building a starting point in FSI computations, ways of accounting for fluid forces acting on structural components that are not expected to influence the flow, adaptive HMGP, and multiscale sequentially coupled FSI techniques. While FSI modeling of complex parachutes was the motivation behind developing some of these techniques, they are also applicable to other classes of complex FSI problems. We also present new ideas to increase the scope of our FSI and CFD techniques. Copyright (C) 2009 John Wiley & Sons, Ltd.

The stabilized space-time fluid-structure interaction (SSTFSI) technique was applied to arterial FSI problems soon after its development by the Team for Advanced Flow Simulation and Modeling. The SSTFSI technique is based on the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation and is supplemented with a number of special techniques developed for arterial FSI. The special techniques developed in the recent past include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, Sequentially Coupled Arterial FSI technique, using layers of refined fluid mechanics mesh near the arterial walls, and a special mapping technique for specifying the velocity profile at inflow boundaries with non-circular shape. In this paper we introduce some additional special techniques, related to the projection of fluid-structure interface stresses, calculation of the wall shear stress (WSS), and calculation of the oscillatory shear index. In the test computations reported here, we focus on WSS calculations in FSI modeling of a patient-specific middle cerebral artery segment with aneurysm. Two different structural mechanics meshes and three different fluid mechanics meshes are tested to investigate the influence of mesh refinement on the WSS calculations.

Computation of incompressible flows in arterial fluid mechanics, especially because it involves fluid-structure interaction, poses significant numerical challenges. Iterative solution of the fluid mechanics part of the equation systems involved is one of those challenges, and we address that in this paper, with the added complication of having boundary layer mesh refinement with thin layers of elements near the arterial wall. As test case, we use matrix data from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm. It is well known that solving linear systems that arise in incompressible flow computations consume most of the time required by such simulations. For solving these large sparse nonsymmetric systems, we present effective preconditioning techniques appropriate for different stages of the computation over a cardiac cycle.

Multiscale versions of the Sequentially-Coupled Arterial Fluid-Structure Interaction (SCAFSI) technique are presented. The SCAFSI technique was introduced as an approximate FSI approach in arterial fluid mechanics. It is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. First we compute a "reference" arterial deformation as a function of time, driven only by the blood pressure profile of the cardiac cycle. Then we compute a sequence of updates involving mesh motion, fluid dynamics calculations, and recomputing the arterial deformation. The SCAFSI technique was developed and tested in conjunction with the stabilized space-time FSI (SSTFSI) technique. Beyond providing a computationally more economical alternative to the fully coupled arterial FSI approach, the SCAFSI technique brings additional flexibility, such as being able to carry out the computations in a spatially or temporally multiscale fashion. In the test computations reported here for the spatially multiscale versions of the SCAFSI technique, we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images. The arterial structure is modeled with the continuum element made of hyperelastic (Fung) material.

The stabilized space time fluid structure interaction (SSTFSI) technique developed by the team for advanced flow simulation and modeling is applied to the computation of arterial fluid structure interaction (FSI) with patient-specific data. The SSTFSI technique is based on the deforming-spatial-domain/stabilized space time formulation and is supplemented with a number of special techniques developed for arterial FSI. These include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, layers of refined fluid mechanics mesh near the arterial walls, and a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape. In the test computations reported here, we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images. Copyright (C) 2009 John Wiley & Sons, Ltd.

The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourthorder accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies. (C) 2007 Elsevier Inc. All rights reserved.

The constrained interpolation profile/cubic interpolated pseudo-particle (CIP) combined unified procedure (CCUP) method (J Phys. Soc. Jpn. 1991; 60:2105-2108), which is based on the CIP method (J. Comput. Phys. 1985: 61:261-268; J Comput. Phys. 1987; 70:355-372; Comput. Phys. Commun. 1991; 66:219-232; J Comput. Phys. 2001; 169:556-593) and the adaptive Soroban grid technique (J. Comput. Phys. 2004; 194:55-77) were combined in (Comput. Mech. 2006; published online) for computation of 3D fluid-object and fluid-structure interactions in the presence of free surfaces and fluid-fluid interfaces. Although the grid system is unstructured, it still has a very simple data structure and this facilitates computational efficiency. Despite the unstructured and collocated features of the grid, the method maintains high-order accuracy and Computational robustness. Furthermore, the meshless feature of the combined technique brings freedom from mesh moving and distortion issues. In this paper, the combined technique is extended to ship hydrodynamics computations. We introduce a new way of computing the advective terms to increase the efficiency in that part of the computations. This is essential in ship hydrodynamics computations where the level of grid refinement needed near the ship Surface and at the free surface results in very large grid sizes. The test cases presented are a test computation with a wave-making wedge and simulation of the hydrodynamics of a container ship. Copyright (c) 2007 John Wiley & Sons, Ltd.

The CIP Method [J comput phys 61:261-268 1985; J comput phys 70:355-372, 1987; Comput phys commun 66:219-232 1991; J comput phys 169:556-593, 2001] and adaptive Soroban grid [J comput phys 194:57-77, 2004] are combined for computation of three- dimensional fluid-object and fluid-structure interactions, while maintaining high-order accuracy. For the robust computation of free-surface and multi-fluid flows, we adopt the CCUP method [Phys Soc Japan J 60:2105-2108 1991]. In most of the earlier computations, the CCUP method was used with a staggered-grid approach. Here, because of the meshless nature of the Soroban grid, we use the CCUP method with a collocated-grid approach. We propose an algorithm that is stable, robust and accurate even with such collocated grids. By adopting the CIP interpolation, the accuracy is largely enhanced compared to linear interpolation. Although this grid system is unstructured, it still has a very simple data structure.

We provide an overview of how fluid-solid and fluid-fluid interfaces can be computed successfully with the constrained interpolation profile/cubic interpolated pseudo-particle (CIP) method (J. Comput. Phys. 1985; 61:261-268; Comput. Phys. Commun. 1991; 66:219-232; Comput. Phys. Commun. 1991; 66: 23j-242: J. Comput. Phys. 2001; 169:556-593) based on adaptive Soroban grids (J. Comput. Phys. 2004; 194:57-77). In this approach, the CIP combined unified procedure (CCUP) technique (J. Phys. Soc. Jpn 1991; 60:2105-2108), which is based on the CIP method, is combined with the adaptive Soroban and technique. One of the superior features of the approach is that even though the grid system is unstructured, it still has a simple data structure that renders remarkable computational efficiency. Another superior feature is that despite the unstructured and collocated nature of the grid, high-order accuracy and computational robustness are maintained. In addition, because the Soroban grid technique does not have any elements or cells connecting the grid points, the approach does not involve mesh distortion limitations. While the details of the approach and several numerical examples were reported in (Comput. Mech. 2006: published online), our objective in this paper is to provide an easy-to-follow description of the key aspects of the approach. Copyright (c) 2007 John Wiley & Sons, Ltd.

A conservative form of Interpolated Differential Operator (IDO) scheme (IDO-CF) is presented for compressible and incompressible fluid dynamics. Fluid equations are solved for multi-moments those are volume integral, surface integral, line integral, and point value of conservative quantities. For Riemann problems of compressible fluid flow, the IDO-CF scheme gives the same or better results compared with Riemann solvers. Direct Numerical Simulation of incompressible turbulent flow shows that the proposed scheme has better resolution than that of non-conservative form of the IDO scheme.

In the regime of finite-difference solutions for Maxwell's equations, all kinds of methods like FDTD (Finite-Difference Time-Domain) method, LBS (Linear Bicharacteristics Scheme) and so on, have been standard. However, in order to deal with large scale and complicated structure in future, higher order scheme and adaptive mesh that does not lose accuracy are required. In this paper, we propose the new method that uses the CIP (constrained interpolation profile/cubic interpolated propagation) method in combination with the numerical method of characteristics (hereafter, CIP-MOC) and the Soroban grid.

The Cubic-Interpolated Propagation/Constrained Interpolation Profile (CIP) method is applied to the fluid-structure interaction like swimming fish and skimmer in the Cartesian grid system. These subjects require accurate calculation of pressure on the surface of the moving body. Using the accurate profile of pressure inside a grid cell, we estimate the force acting on the rigid body even if the rigid body has a structure in a scale smaller than grid cell. The CIP method is used to define such subgrid-scale structure. The experiments are performed to show the accuracy of the simulations. (C) 2005 Published by Elsevier Ltd.

We review some recent progress of the CIP method that is known as a general numerical solver for solid, liquid, gas and plasmas. This method is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. Some applications to skimmer, swimming fish and laser cutting are presented. This method is recently extended to almost mesh-free system that is called 'soroban grid' that ensures the third-order accuracy both in time and space with the help of the CIP method. Copyright (C) 2005 John Wiley Sons, Ltd.

A new numerical scheme to solve a water flow with a free water surface and arbitrary curved ground surface is proposed. In the proposed method, by using a soroban grid system proposed by one of the authors, computational mesh is reconstruct easily at each time step so that some grid points locate on a free water surface exactly. Time development of velocity components and water surface are calculated according to an incompressible inviscid flow equation without any transformation of the equation. Advection effects are calculated by direct interpolation of the CIP method in 3rd order accuracy in spatial. After the advection is solved, acceleration of velocity components due to the pressure gradient is solved using a FDM approach on a soroban grid system. The proposed method is applied to some problems and computational results are examined through comparisons with results of other FDM scheme and theoretical result.

We propose a new algorithm for producing computer graphics of melting and evaporation process of matter. Such a computation becomes possible by a universal solver for solid, liquid and gas based on the CIP (Cubic-Interpolated Propagation / Constrained Interpolation Profile) method proposed by one of the authors. This method can also be applied to the movement, deformation and even break up of solid, liquid and gas in one simple algorithm. Therefore seamless computation of all the phases of matter becomes possible. This enables us to reproduce natural phenomena in some instances by computation. In order to demonstrate this reality, we show how precisely the computational result replicates the movies of real phenomena. The flattering motions of metal disk in water and thin name card in air are treated showing accuracy of force calculation on the surface of sub-grid scale. Although the CIP uses semi-Lagrangian form algorithm, the exact mass conservation is guaranteed by additional tool. By using this scheme, separation of a bubble in bifurcation tube and splashing of water surface are successfully simulated.

A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (&gt;10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated. (C) 2003 Elsevier B.V. All rights reserved.

We propose a scheme that has the third-order accuracy both in time and space, and can be used in curvilinear system. The method is based on the CIP method and Soroban grid. Although the mesh is used tentatively, it does not need the connectivity of the grid and is a class of mesh-less scheme. Some benchmark test programs are proposed to check the accuracy in curvilinear coordinate.

We present a review of the CIP method, which is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of semi-Lagrangian scheme. Comprehensive review is given for the strategy of the CIP method that has a compact support and subcell resolution including front capturing algorithm with functional transformation. (C) 2002 Elsevier Science B.V. All rights reserved.

We present a review of the CIP method, which is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of semi-Lagrangian scheme. Comprehensive review is given for the strategy of the CIP method that has a compact support and subcell resolution including front capturing algorithm with functional transformation. (C) 2002 Elsevier Science B.V. All rights reserved.

A new numerical method that guarantees exact mass conservation is proposed to solve multi-dimensional hyperbolic equations in semi-Lagrangian form without directional splitting. The method is based on a concept of CIP scheme and keep the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variable. Although the advection and non-advection terms are separately treated, the mass conservation is kept in a form of spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian schemes with exact conservation that has been beyond the capability of conventional semi-Lagrangian schemes. (C) 2002 Elsevier Science B.V. All rights reserved.

A new numerical method that guarantees exact mass conservation is proposed to solve multi-dimensional hyperbolic equations in semi-Lagrangian form without directional splitting. The method is based on a concept of CIP scheme and keep the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variable. Although the advection and non-advection terms are separately treated, the mass conservation is kept in a form of spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian schemes with exact conservation that has been beyond the capability of conventional semi-Lagrangian schemes. (C) 2002 Elsevier Science B.V. All rights reserved.

We present a review of the CIP method, which is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of semi-Lagrangian scheme. Comprehensive review is given for the strategy of the CIP method that has a compact support and sub-cell resolution including front capturing algorithm with functional transformation.