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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.

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.

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*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).

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. .

We present a new space-time SUPG formulation of the shallow-water equations. In this formulation, we use a stabilization parameter that was introduced for compressible flows and a new shock-capturing parameter. In the context of two test problems, we evaluate the performance of the new shock-capturing parameter. We also evaluate the performance of the space-time SUPG formulation compared to the semi-discrete SUPG formulation, where the system of semi-discrete equations is solved with the central-difference (Crank-Nicolson) time-integration algorithm.

A stabilized finite element formulation for the computation of turbulent reacting flows and NOx emission is presented. The method is based on the Streamline-Upwind/Petrov–Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) formulations, complemented with directionally formulated diffusion for reaction-dominated flows (‘DRDJ’ stabilization). The stabilized formulation is applied to the advection–diffusion–reaction equations governing the turbulent combustion and the NOx emission equations based on the thermal and the N2O pathways. The simulation is carried out for a co-axial burner, with a non-premixed swirling flame. The burner is operated at high pressure to represent the take-off conditions for an aero-engine. The vortical patterns of the swirling flame are analyzed together with the temperature field and flame position. The NOx formation processes are discussed, providing insight into the features of thermal and N2O mechanisms. Copyright © 2010 John Wiley & Sons, Ltd.

We review and summarize our research activities in fluid-structure interaction (FSI) analysis of cerebral aneurysms using anatomically realistic geometry models based on medical images. Emphasis is placed on influencing factors in computational FSI, and their role and clinical implications are discussed in terms of the wall shear stress (WSS). The key factors are: (1) arterial and aneurysm geometries, (2) wall structure modeling, (3) blood pressure, (4) outflow conditions and (5) inflow conditions. Among these, we find the impact of the arterial and aneurysm geometries to be the most significant. Blood pressure also has a significant impact on the WSS distribution; a hypothetical hypertensive blood pressure condition could help estimate the rupture risk for an aneurysm. We find the other three factors to be minor compared with the arterial and aneurysm geometries and blood pressure, although the level of influence could be unique to the middle cerebral artery aneurysms that we have been focusing on in our studies.

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.

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 © 2010 John Wiley & Sons, Ltd.

We provide a brief chronological background on the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation, its use in aerodynamic modeling of a paratrooper separating from an aircraft, and the fluid–object interactions subcomputation technique (FOIST). Copyright © 2010 John Wiley & Sons, Ltd.

Some comments are provided on the shock-capturing techniques and stabilization parameters used in a recent paper (B.S. Kirk, Int. J. Numer. Meth. Fluids 2009; DOI: 10.1002/fld.2195) in conjunction with the SUPG formulation of compressible flows. Copyright © 2010 John Wiley & Sons, Ltd.

The objective of this paper is to show that use of the element-vector-based definition of stabilization parameters, introduced in [T.E. Tezduyar, Computation of moving boundaries and interfaces and stabilization parameters, Int. J. Numer. Methods Fluids 43 (2003) 555–575; T.E. Tezduyar, Y. Osawa, Finite element stabilization parameters computed from element matrices and vectors, Comput. Methods Appl. Mech. Engrg. 190 (2000) 411–430], circumvents the well-known instability associated with conventional stabilized formulations at small time steps. We describe formulations for linear advection–diffusion and incompressible Navier–Stokes equations and test them on three benchmark problems: advection of an L-shaped discontinuity, laminar flow in a square domain at low Reynolds number, and turbulent channel flow at friction-velocity Reynolds number of 395.

The Sequentially-Coupled Arterial Fluid–Structure Interaction (SCAFSI) technique is one of the special techniques developed recently by the Team for Advanced Flow Simulation and Modeling (T☆AFSM) for FSI modeling of blood flow and arterial dynamics. The SCAFSI technique, which was introduced as an approximate FSI approach in arterial fluid mechanics, is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. In the SCAFSI, 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. Although the SCAFSI technique was developed and tested in conjunction with the stabilized space–time FSI (SSTFSI) technique, it can also be used in conjunction with other FSI modeling techniques categorized as moving-mesh methods. The SSTFSI technique is based on the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation and includes the enhancements introduced recently by the T☆AFSM. The arterial structures can be modeled with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element can be made of linearly-elastic or hyperelastic material (Mooney–Rivlin or Fung). Here we provide an overview of the SCAFSI technique and present a number of test computations for abdominal aortic and cerebral aneurysms, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data.

We present applications of the stabilized finite element formulations developed for incompressible flows with thermal coupling to 2D and 3D test problems. The stabilized formulations are based on the streamline-upwind/Petrov–Galerkin and pressure-stabilizing/Petrov–Galerkin stabilizations and are supplemented with discontinuity capturing (DC), including the discontinuity-capturing directional dissipation. The stabilization and DC parameters associated with these formulations are also presented. The coupled fluid mechanics and temperature equations are solved with a direct coupling technique. The test problems computed include 2D and 3D natural convection, as well as a simplified 3D model of air circulation in a small data center. Copyright © 2008 John Wiley & Sons, Ltd.

We present an overview of how the arterial fluid mechanics problems can be modeled with the stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM). The SSTFSI technique includes the enhancements introduced recently by the T★AFSM to increase the scope, accuracy, robustness and efficiency of this class of techniques. The SSTFSI technique is supplemented with a number of special techniques developed for arterial fluid mechanics modeling. These include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, and the sequentially coupled arterial FSI (SCAFSI) technique. The recipe for pre-FSI computations is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. The SCAFSI technique, which was introduced as an approximate FSI approach in arterial fluid mechanics, is also based on that assumption. The need for an estimated zero-pressure arterial geometry is based on recognizing that the patient-specific image-based geometries correspond to time-averaged blood pressure values. In our arterial fluid mechanics modeling the arterial walls can be represented with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element is made of hyperelastic (Fung) material. Test computations are presented for cerebral and abdominal aortic aneurysms, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data. Copyright © 2007 John Wiley & Sons, Ltd.

The YZp shock-capturing technique was introduced recently for use in combination with the streamline-upwind/Petrov-Galerkin formulation of compressible flows in conservation variables. The YZβ shock-capturing parameter is much simpler than an earlier parameter derived from the entropy variables for use in conservation variables. In this paper, we propose to use the YZβ shock-capturing in combination with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. We evaluate the performance of the V-SGS and YZβ combination in a number of standard, 2D test problems. Compared to the earlier shock-capturing parameter derived from the entropy variables, in addition to being much simpler, the YZβ shock-capturing parameter yields better shock quality in these test problems.

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; 66:233–242; 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 grid 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 © 2007 John Wiley & Sons, Ltd.

The stabilized space-time fluid-structure interaction (SSTFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) are applied to FSI modelling in arterial fluid mechanics. Modelling of flow in arteries with aneurysm is emphasized. The SSTFSI techniques used are based on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation and include the enhancements introduced recently by the T*AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The arterial structures can be modelled with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element can be made of linearly elastic or hyperelastic material. Test computations are presented for cerebral and abdominal aortic aneurysms and carotid-artery bifurcation, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data.

We propose a numerical model for computation of flow problems that involve both fluid-solid and fluid-fluid interfaces. The model is based on the mixed interface-tracking/interface-capturing technique (MITICT), which was introduced earlier for problems that involve both fluid-solid interfaces that are accurately tracked with a moving mesh method and fluid-fluid interfaces that are too complex to track and therefore treated with an interface-capturing technique. In our numerical model, fluid-solid interfaces are handled with the moving Lagrangian interface technique (MLIT) and fluid-fluid interfaces with the edge-tracked interface locator technique (ETILT). The mixed technique is tested in computation of a fluid-particle interaction problem in the presence of a fluid-fluid interface impacted by the particle.

The YZβ discontinuity-capturing operator, recently introduced in (Encyclopedia of Computational Mechanics, Vol. 3, Fluids. Wiley: New York, 2004) in the context of compressible flows, is applied to a time-dependent, scalar advection-diffusion equation with the purpose of modelling drug delivery processes in blood vessels. The formulation is recast in a residual-based form, which reduces to the previously proposed formulation in the limit of zero diffusion and source term. The NURBS-based isogeometric analysis method, proposed by Hughes et al. (Comput. Methods Appl. Mech. Eng. 2005; 194:4135-4195), was used for the numerical tests. Effects of various parameters in the definition of the FZβ operator are examined on a model problem and the better performer is singled out. While for low-order B-spline functions discontinuity capturing is necessary to improve solution quality, we find that high-order, high-continuity B-spline discretizations produce sharp, nearly monotone layers without the aid of discontinuity capturing. Finally, we successfully apply the YZβ approach to the simulation of drug delivery in patient-specific coronary arteries.

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.

Fluid-structure interaction (FSI) computations of two cerebral aneurysms are carried out under hypertensive and normotensive blood pressures. Hypertensive blood pressure is one of the major risk factors in subarachnoid hemorrhage, which is mostly caused by the rupture of cerebral aneurysm. Since hemodynamic wall shear stress (WSS) is known to play an important role in aneurysm progression, investigating the WSS distribution in conjunction with hypertensive blood pressure is expected to provide a better understanding of aneurysms. The WSS distributions obtained from the simulations show that hypertensive blood pressure considerably affects one of the subjects but not the other. The effect is a wider spreading of the high WSS region on the aneurysm wall, which prevents the wall from weakening. It is also shown that the deformation of the aneurysm wall can alter the flow patterns in the aneurysm to diminish the stagnant flow near the apex, which is linked to the weakening of the wall. The effect of hypertensive blood pressure and wall deformation is shown to be highly dependent on individual aneurysm geometry, and that stresses the importance of subject-specific simulations.

We provide an overview of some of the interface-tracking and interface-capturing techniques we developed for finite element computation of flow problems with moving boundaries and interfaces. This category of flow problems includes fluid–particle, fluid–object and fluid–structure interactions; free-surface and two-fluid flows; and flows with moving mechanical components. Both classes of techniques are based on stabilized formulations. The interface-tracking techniques are based on the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation, where the mesh moves to track the interface. The interface-capturing techniques, developed primarily for free-surface and two-fluid interface flows, are formulated typically over non-moving meshes, using an advection equation in addition to the flow equations. The advection equation governs the evolution of an interface function that marks the location of the interface. We also highlight some of the methods we developed to increase the scope and accuracy of these two classes of techniques.

We describe the space–time finite element techniques we developed for computation of fluid–structure interaction (FSI) problems. Among these techniques are the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation and its special version, and the mesh update methods, including the solid-extension mesh moving technique (SEMMT). Also among these techniques are the block-iterative, quasi-direct and direct coupling methods for the solution of the fully discretized, coupled fluid and structural mechanics equations. We present some test computations for the mesh moving techniques described. We also present numerical examples where the fluid is governed by the Navier– Stokes equations of incompressible flows and the structure is governed by the membrane and cable equations. Overall, we demonstrate that the techniques we have developed have increased the scope and accuracy of the methods used in computation of FSI problems. � 2005 Elsevier B.V. All rights reserved.

The streamline-upwind/Petrov–Galerkin (SUPG) formulation is one of the most widely used stabilized methods in finite element computation of compressible flows. It includes a stabilization parameter that is known as “τ”. Typically the SUPG formulation is used in combination with a shock-capturing term that provides additional stability near the shock fronts. The definition of the shock-capturing term includes a shock-capturing parameter. In this paper, we describe, for the finite element formulation of compressible flows based on conservation variables, new ways for determining the τ and the shock-capturing parameter. The new definitions for the shock-capturing parameter are much simpler than the one based on the entropy variables, involve less operations in calculating the shock-capturing term, and yield better shock quality in the test computations.

We provide an overview of the role of parallel finite element computations in fluid mechanics. We emphasize the class of flow problems involving moving boundaries and interfaces. Some of the computationally most challenging flow problems, such as fluid–object and fluid–structure interactions as well as free-surface and two-fluid flows, belong to this class. In the development of the methods targeting this class of problems, the computational challenges involved need to be addressed in such a way that 3D computation of complex applications can be carried out efficiently on parallel computers. This requirement has to be one of the key factors in designing various components of the overall solution approach, such as solution techniques for the discretized equations and mesh update methods for handling the changes in the spatial domain occupied by the fluid. This overview includes a description of how the computational challenges are addressed and how the computational schemes can be enhanced with special preconditioning techniques.

Hemodynamic factors such as the wall shear stress are believed to affect a number of cardiovascular diseases including atherosclerosis and aneurysm. Since resolving phenomena in a living human body is currently beyond the capabilities of in vivo measurement techniques, computer modeling is expected to play an important role in gaining a better understanding of the relationship between the cardiovascular diseases and the hemodynamic factors. We have developed a computer modeling technique for cardiovascular hemodynamic simulations. With this modeling technique, patient-specific 3D geometry of an artery can be analyzed. We take into account some of the important factors in human body for the purpose of demonstrating in vivo situations in a virtual world. The interaction between the blood flow and the deformation of the arterial walls is a factor that we are specifically focusing on. For such fluid–structure interactions, we have developed a computer modeling tool based on the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation. This simulation tool is applied to a patient-specific model under pulsatile blood flow conditions. The simulations show that the flow behavior with compliant arterial walls is different from what we see with rigid arterial walls. Consequently, the distribution of the wall shear stress on the compliant arterial walls is significantly different from that on the rigid arterial walls. We deduce that the compliance of the arterial walls needs to be taken into account in cardiovascular hemodynamic simulations, and the computer modeling tool we have developed can be effective in investigation of cardiovascular diseases.

Two preconditioners are presented for equation systems of strongly coupled fluid–structure interaction computations where the structure is modeled by shell elements. These preconditioners fall into the general category of incomplete LU factorization. The two differ mainly in whether the coefficient matrix is factorized node by node or variable-by-variable. In the variable-wise preconditioner, a modified Schur complement system for pressure is solved approximately with a few iterations using a special preconditioner. The efficiencies of the two preconditioners are compared for different finite element formulations of the fluid mechanics part, including formulations with SUPG and PSPG stabilizations.

Soft landing of a payload with the aid of a retraction device is an important aspect in cargo parachute operations. Accurate simulation of this class of parachute operations with a computer model that takes into account the fluid–structure interactions involved would complement drop tests and support the design of cargo parachute systems. We describe the computational methods developed for this purpose, demonstrate how the computational model works in investigation of different soft-landing conditions, and show a good correlation between the data from our simulations and drop tests. Copyright © 2004 John Wiley & Sons, Ltd.

The enhanced-discretization successive update method (EDSUM) is a multi-level iteration method designed for computation of the flow behaviour at small scales. As an enhancement in iterative solution of non-linear and linear equation systems, the EDSUM is one of the enhanced discretization and solution techniques developed for more effective computation of complex flow problems. It complements techniques based on enhancement in spatial discretization and based on enhancement in time discretization in the context of a space-time formulation. It is closely related to the enhanced-discretization interface-capturing technique (EDICT), as the function spaces used in the EDSUM are very similar to those used in the EDICT. The EDSUM also has a built-in mechanism for transferring flow information between the large and small scales in a fashion consistent with the discretizations resulting from the underlying stabilized formulations. With a number of test computations for steady-state problems governed by the advection-diffusion equation, we demonstrate that the EDSUM has the potential to become a competitive technique for computation of flow behaviour at small scales

In computation of fluid–structure interactions involving large displacements, we use a mesh update method composed of mesh moving and remeshing-as-needed. For problems with complex geometries, we need automatic mesh moving techniques that reduce the need for remeshing. We also would like that these mesh moving techniques allow us to control mesh resolution near the fluid–structure interfaces so that we can represent the boundary layers more accurately. In the mesh moving techniques we designed, the motion of the nodes is governed by the equations of elasticity, and mesh deformation is handled selectively based on element sizes and deformation modes. This is helping us reduce the frequency of remeshing. With the solid-extension mesh moving technique presented in this paper, we are also able to limit mesh distortion in thin layers of elements placed near fluid–structure interfaces.

We investigate, for linear and higher-order elements, various ways of calculating the advective limit of the stabilization parameter (“ τ ”) used in the streamline-upwind/Petrov–Galerkin (SUPG) formulation of flow problems. In the context of a pure advection test problem, we compare the “UGN-based”, element-matrix-based, and element-node-based calculations of the advective limit of the τ . Our investigation shows that the performances of the “UGN-based” and element-matrix-based τ definitions are comparable, with the element-matrix-based definition yielding somewhat lower τ values. We also show that for both definitions, as the polynomial orders increase, the τ values decrease, as they should.

The enhanced discretization and solution techniques are among the advanced computational methods we rely on in simulation and modeling of complex flow problems, including those with moving boundaries and interfaces. The set of enhanced discretization and solution techniques includes those based on enhancement in spatial discretization, enhancement in time discretization, and enhancement in iterative solution of nonlinear and linear equation systems. The enhanced-approximation linear solution technique (EALST) was introduced to increase the performance of the iterative technique used in solution of the linear equation systems when some parts of the computational domain may offer more of a challenge for the iterative method than the others. The EALST can be used for computations based on semi-discrete or space–time formulations.

The enhanced-discretization space–time technique (EDSTT) was developed for the purpose of being able to, in the context of a space–time formulation, enhance the time-discretization in regions of the fluid domain requiring smaller time steps. Such requirements are often encountered in time-accurate computations of fluid–structure interactions, where the time-step size required by the structural dynamics part is smaller, and carrying out the entire computation with that time-step size would be too inefficient for the fluid dynamics part. In the EDSTT-single-mesh (EDSTT-SM) approach, a single space–time mesh, unstructured both in space and time, would be used to enhance the time-discretization in regions requiring smaller time steps. In the EDSTT-multi-mesh (EDSTT-MM) approach, we complement the space–time concept of the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation with the multi-mesh concept of the enhanced-discretization interface-capturing technique (EDICT). In applications to fluid–structure interactions, the structural dynamics modeling is based on a single space–time mesh and the fluid dynamics modeling is based on two space–time meshes. The structural dynamics interface nodes in the space–time domain also belong to the second fluid mesh, which accommodates the time-step requirement of the structural dynamics. We apply the EDSTT-SM and EDSTT-MM approaches to a number of test problems to demonstrate how these methods work and why they would be desirable to use in time-accurate computations.

Recently, it is reported that risk of rupture of aneurysms is further less than risk of surgical complications. Therefore, to avoid unnecessary surgical operations, prediction of rupture of aneurysms is necessary. Because wall shear stress is known to play an important role for a vascular disease, the authors have investigated the relationship between wall shear stress and cerebral aneurysms. In this paper, numerical fluid-structure interaction analyses are performed to investigate influences of wall deformation on hemodynamic factors. The results show several patterns of arterial wall deformations and their influences on blood flow behavior and hemodynamic factors.

For the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations for flow problems, we present in this paper a comparative study of the stabilization parameters defined in different ways. The stabilization parameters are closely related to the local length scales (“element length”), and our comparisons include parameters defined based on the element-level matrices and vectors, some earlier definitions of element lengths, and extensions of these to higher-order elements. We also compare the numerical viscosities generated by these stabilized formulations with the eddy viscosity associated with a Smagorinsky turbulence model that is based on element length scales.

Aerodynamic interactions between parachute canopies can occur when two separate parachutes come close to each other or in a cluster of parachutes. For the case of two separate parachutes, our computational study focuses on the effect of the separation distance on the aerodynamic interactions, and also focuses on the fluid-structure interactions with given initial relative positions. For the aerodynamic interactions between the canopies of a cluster of parachutes, we focus on the effect of varying the number and arrangement of the canopies.

The interface-tracking and interface-capturing techniques we developed in recent years for computation of flow problems with moving boundaries and interfaces rely on stabilized formulations such as the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods. The interface-tracking techniques are based on the deforming-spatial-domain/stabilized space-time formulation, where the mesh moves to track the interface. The interface-capturing techniques, typically used with non-moving meshes, are based on a stabilized semi-discrete formulation of the Navier-Stokes equations, combined with a stabilized formulation of the advection equation governing the time-evolution of an interface function marking the interface location. We provide an overview of the interface-tracking and interface-capturing techniques, and highlight how we determine the stabilization parameters used in the stabilized formulations

In computation of fluid-structure interactions, we use mesh update methods consisting of mesh-moving and remeshing-as-needed. When the geometries are complex and the structural displacements are large, it becomes even more important that the mesh moving techniques are designed with the objective to reduce the frequency of remeshing. To that end, we present here mesh moving techniques where the motion of the nodes is governed by the equations of elasticity, with selective treatment of mesh deformation based on element sizes as well as deformation modes in terms of shape and volume changes. We also present results from application of these techniques to a set of two-dimensional test cases.

In this paper we describe a computational technique for simulation of the fluid–structure interactions of a parachute crossing the far wake of an aircraft. This technique relies on using the long-wake flow data already computed, in our case, with the Multi-Domain Method (MDM) we developed earlier. The fluid–structure interaction computations are carried out over a domain enclosing the parachute and moving with the payload. This domain functions as one of the subdomains of the MDM designed specifically for the parachute fluid–structure interactions considered here. The boundary conditions for this subdomain are extracted from the long-wake flow data, at locations corresponding to the positions of those boundaries in the subdomain over which the wake flow data were computed. The Navier–Stokes equations of incompressible flows, governing the fluid dynamics, are solved with the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation, which can handle changes in the spatial domain occupied by the fluid. This formulation is coupled to the finite element formulation used for solving the membrane equations governing the structural mechanics of the parachute canopy and the equations governing the mechanics of the suspension lines. The numerical example included demonstrates how the technique described here, functioning as a component of the MDM, enables us to simulate the fluid–structure interactions of a parachute crossing an aircraft wake.

The dynamics of parachutes involves complex interaction between the parachute structure and the surrounding flow field. Accurate representation of parachute systems requires treatment of the problem as a fluid–structure interaction (FSI). In this paper we present the numerical simulations we performed for the purpose of comparison to a series of cross-parachute wind tunnel experiments. The FSI model consists of a 3-D fluid dynamics (FD) solver based on the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) procedure, a structural dynamics (SD) solver, and a method of coupling the two solvers. These FSI simulations include the prediction of the coupled FD and SD behavior, drag histories, flow fields, structural behavior, and equilibrium geometries for the structure. Comparisons between the numerical results and the wind tunnel data are conducted for three cross-parachute models and at three different wind tunnel flow speeds.

In this paper, an enhanced finite element formulation for unsteady incompressible flows with moving interfaces is presented. The weak form of the Navier–Stokes equations, written using a generalized streamline operator technique, is coupled with the movement of the interface between two immiscible fluids defined through an independent moving mesh. The position of the interface is updated using a Lagrangian formulation. In this framework, a global mass conservation corrector algorithm and an enhanced element integration technique are proposed to improve accuracy. The method is applied to a number of test problems with moving interfaces.

We present the multi-domain method (MDM) for computation of unsteady flow past a cargo aircraft and around a parachute crossing the aircraft's far wake. The base computational methods used here are the stabilized semi-discrete and space-time finite element formulations developed earlier. In the MDM, the computational domain is divided into an ordered sequence of overlapping subdomains. The flow field computed over Subdomain-1, which contains the aircraft, supplies the inflow boundary conditions for Subdomain-2, which is used for computing the long-wake flow. Subdomain-3 contains the parachute, and moves across Subdomain-2. The boundary conditions for Subdomain-3 are extracted from the flow field computed over Subdomain-2, at locations corresponding to the positions of the boundaries of Subdomain-3 as it crosses Subdomain-2. The computation over Subdomain-1, which contains a complex but fixed object, is based on a general-purpose implementation of the semi-discrete formulation. The computation over Subdomain-2, which contains no objects, is based on a special-purpose implementation that exploits the simplicity of the mesh to increase the computational speed. The computation over Subdomain-3, which contains a complex and moving object, is based on a general-purpose implementation of the space-time formulation. With a numerical example, we show that different methods can be brought together in the context of the MDM to address the computational challenges involved in the aerodynamics of a parachute crossing the far wake of an aircraft.

In this paper we present a 3D computational technique for simulation of complex, real-world flow problems with fast-rotating mechanical components. This technique is based on the Deformable-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, Shear-Slip Mesh Update Method (SSMUM), and an efficient parallel implementation for distributed-memory parallel computing platforms. The DSD/SST formulation was developed earlier for flow problems with moving boundaries and interfaces, including flows with moving mechanical components. The DSD/SST formulation requires, as a companion method, an effective mesh update strategy, especially in complex flow problems. The SSMUM was developed to meet the mesh update requirements in simulation of flow problems with fast translations, and recently, with a new version of SSMUM, fast rotations. As an example of the class of challenging simulations that can be carried out by this technique, we present computation of flow around a helicopter with its rotor in motion.

We present computational methods for 3D simulation of fluid–object interactions in spatially periodic flows. These methods include a stabilized space-time finite element formulation for incompressible flows with spatial periodicity, automatic mesh generation and update techniques for fluid–object mixtures with spatial periodicity, and parallel implementations. The methods can be applied to uni-periodic (i.e., periodic in one direction), bi-periodic, or tri-periodic flows. The methods are described here in the context of tri-periodic flows with fluid–object interactions, and are applied to the simulation of sedimentation of particles in a fluid. We present several case studies where the results obtained provide notable insight into the behavior of fluid–particle mixtures during sedimentation.

We propose new ways of computing the stabilization parameters used in the stabilized finite element methods such as the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) formulations. The parameters are computed based on the element-level matrices and vectors, which automatically take into account the local length scales, advection field and the Reynolds number. We describe how we compute these parameters in the context of first a time-dependent advection–diffusion equation and then the Navier–Stokes equations of unsteady incompressible flows.

We present a parallel finite element computational method for 3D simulation of fluid–structure interactions (FSI) in parachute systems. The flow solver is based on a stabilized finite element formulation applicable to problems involving moving boundaries and governed by the Navier–Stokes equations of incompressible flows. The structural dynamics (SD) solver is based on the total Lagrangian description of motion, with cable and membrane elements. The nonlinear equation system is solved iteratively, with a segregated treatment of the fluid and SD equations. The large linear equation systems that need to be solved at every nonlinear iteration are also solved iteratively. The parallel implementation is accomplished using a message-passing programming environment. As a test case, the method is applied to computation of the equilibrium configuration of an anchored ram-air parachute placed in an air stream.

We present a parallel computational strategy for carrying out 3-D simulations of parachute fluid–structure interaction (FSI), and apply this strategy to a round parachute. The strategy uses a stabilized space-time finite element formulation for the fluid dynamics (FD), and a finite element formulation derived from the principle of virtual work for the structural dynamics (SD). The fluid–structure coupling is implemented over compatible surface meshes in the SD and FD meshes. Large deformations of the structure are handled in the FD mesh by using an automatic mesh moving scheme with remeshing as needed.

We present the stabilized-finite-element/interface-capturing (SFE/IC) method developed for parallel computation of unsteady flow problems with two-fluid interfaces and free surfaces. The SFE/IC method involves stabilized formulations, an interface-sharpening technique, and the enforcement of global mass conservation for each fluid. The SFE/IC method has been efficiently implemented on the CRAY T3E parallel supercomputer. A number of 2D test problems are presented to demonstrate how the SFE/IC method works and the accuracy it attains. We also show how the SFE/IC method can be very effectively applied to 3D simulation of challenging flow problems, such as two-fluid interfaces in a centrifuge tube and operational stability of a partially filled tanker truck driving over a bump.

We present the 3D implementation and applications of the enhanced-discretization interface-capturing technique (EDICT) in computation of unsteady flows with two-fluid interfaces. In such computations, EDICT can be used as a very effective method, which combines the flexibility and efficiency of interface-capturing techniques with the accuracy provided by enhanced discretization at the interfaces. A stabilized finite element interface-capturing technique is used as the base formulation to solve, over a typically non-moving mesh, the Navier–Stokes equations and an advection equation governing the interface function. To increase the accuracy in modeling the interfaces, we use finite element functions with multiple components at and near the interfaces, with each component coming from a different level of mesh refinement. With its parallel implementation on advanced high-performance computing platforms such as the CRAY T3E, EDICT is a powerful tool for the simulation of a complex, 3D unsteady flow problems with two fluid-interfaces, including free surfaces.