Skip to main content
main-content
Top

About this book

Computational fluid-structure interaction and flow simulation are challenging research areas that bring solution and analysis to many classes of problems in science, engineering, and technology. Young investigators under the age of 40 are conducting much of the frontier research in these areas, some of which is highlighted in this book. The first author of each chapter took the lead role in carrying out the research presented. The topics covered include Computational aerodynamic and FSI analysis of wind turbines,
Simulating free-surface FSI and fatigue-damage in wind-turbine structural systems,
Aorta flow analysis and heart valve flow and structure analysis,
Interaction of multiphase fluids and solid structures,
Computational analysis of tire aerodynamics with actual geometry and road contact, and
A general-purpose NURBS mesh generation method for complex geometries.
This book will be a valuable resource for early-career researchers and students — not only those interested in computational fluid-structure interaction and flow simulation, but also other fields of engineering and science, including fluid mechanics, solid mechanics and computational mathematics – as it will provide them with inspiration and guidance for conducting their own successful research. It will also be of interest to senior researchers looking to learn more about successful research led by those under 40 and possibly offer collaboration to these researchers.

Table of Contents

Frontmatter

Simulating Free-Surface FSI and Fatigue Damage in Wind-Turbine Structural Systems

This article reviews state-of-the-art numerical techniques for fluid–structure interaction (FSI) of full-scale wind-turbine systems. Simulation of floating wind turbines subjected to combined wind-flow and ocean-wave forcing, and modeling of high-cycle fatigue failure of blades due to long-term cyclic aerodynamic loading are the focal points of this article. Computational techniques including advanced structural modeling based on isogeometric analysis (IGA), free-surface FSI, and fatigue-damage modeling are presented. Representative computational examples involving land-based and floating offshore wind-turbine designs illustrate the versatility and power of the computational methods developed.
Y. Bazilevs, J. Yan, X. Deng, A. Korobenko

Aorta Flow Analysis and Heart Valve Flow and Structure Analysis

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.
Kenji Takizawa, Tayfun E. Tezduyar, Hiroaki Uchikawa, Takuya Terahara, Takafumi Sasaki, Kensuke Shiozaki, Ayaka Yoshida, Kenji Komiya, Gaku Inoue

Residual-Based Large Eddy Simulation with Isogeometric Divergence-Conforming Discretizations

Isogeometric divergence-conforming discretizations have recently arisen as an attractive candidate for approximation of the incompressible Navier-Stokes problem. By construction, isogeometric divergence-conforming discretizations yield discrete velocity fields which are pointwise divergence-free, and as a consequence, they admit discrete balance laws for mass, momentum, angular momentum, energy, vorticity, enstrophy, and helicity. It has been demonstrated in previous work that isogeometric divergence-conforming discretizations are simultaneously more accurate and more stable than classical mixed methods when applied to the direct numerical simulation of incompressible fluid flow. In this chapter, we present two new residual-based large eddy simulation methodologies specifically designed for isogeometric divergence-conforming discretizations. The first methodology arises from a structure-preserving variational multiscale analysis of the incompressible Navier-Stokes equations. The second methodology combines ideas from variational multiscale analysis and large eddy simulation methodologies employing an eddy viscosity, yielding a residual-based eddy viscosity method. We develop quasi-static and dynamic models for both methodologies. Numerical results illustrate the new methodologies yield improved results as compared with standard eddy viscosity based approaches when applied to a transitional flow problem.
John A. Evans, Christopher Coley, Ryan M. Aronson, Corey L. Wetterer-Nelson, Yuri Bazilevs

Interaction of Multiphase Fluids and Solid Structures

Fluid–Structure Interaction (FSI) problems are ubiquitous in almost every branch of engineering and science. Their nonlinear and time-dependent nature makes usually the analytical solution very difficult or even impossible to obtain, requiring the use of experimental analysis and/or numerical simulations. This fact has prompted the development of a great variety of numerical methods for FSI. However, most of the efforts have been focused on classical fluids governed by the Navier–Stokes equations, which cannot capture the physical mechanisms behind multiphase fluids. Here, we present several models for the interplay of solids and multiphase flows, which we apply to particular problems such as phase-change-driven implosion, droplet motion, and elastocapillarity.
In this work, the behavior of the structure is described by the nonlinear equations of elastodynamics and treated as a hyperelastic solid. In particular, we employ a Neo-Hookean and a Saint Venant–Kirchhoff model. Our approach for the multiphase fluid is based on the diffuse-interface or phase-field method. The Navier–Stokes–Korteweg equations are used to describe compressible fluids that are composed of two phases of the same component, which may undergo phase transformation. The Navier–Stokes–Cahn–Hilliard equations are used to describe two-component immiscible flows with surface tension. As FSI technique, we adopt a boundary-fitted approach with matching discretization at the interface. This choice leads to a natural monolithic FSI coupling with strong, exact enforcement of the kinematic conditions. We use the Lagrangian description to derive the semidiscrete form of the solid equations and the Arbitrary Lagrangian–Eulerian description for the fluid domain. For the spatial discretization we adopt isogeometric analysis based on Non-Uniform Rational B-Splines. Regarding the time integration, we use a generalized-α scheme. The nonlinear system of equations is solved using a Newton–Raphson iteration procedure, which leads to a two-stage predictor-multicorrector algorithm. A quasi-direct monolithic formulation is adopted for the solution of the FSI problem.
Hector Gomez, Jesus Bueno

Immersogeometric Analysis of Bioprosthetic Heart Valves, Using the Dynamic Augmented Lagrangian Method

In the mid-2010s, we began applying a combination of isogeometric analysis and immersed boundary methods to the problem of bioprosthetic heart valve (BHV) fluid–structure interaction (FSI). This chapter reviews how our research on BHV FSI (1) crystallized the emerging concept of immersogeometric analysis, (2) introduced a new semi-implicit numerical method for weakly enforcing constraints in time dependent problems, which we refer to as the dynamic augmented Lagrangian approach, and (3) clarified the important role of mass conservation in immersed FSI analysis. We illustrate these contributions with selected numerical results and discuss future improvements to, and applications of, the computational FSI techniques we have developed.
Ming-Chen Hsu, David Kamensky

A Numerical Analysis of Rheology of Capsule Suspensions Using a GPU-Accelerated Boundary Element Method

Understanding the behavior of capsules in flow and the rheology of capsule suspensions is of fundamental importance for diverse problems in nature and engineering. The particle Reynolds number of capsules is often small, and the flow field is given by the boundary integral formulation of the Stokes equations. The boundary element method (BEM) based on the boundary integral formulation is thus one of the most accurate methods for simulating capsules under Stokes flow regime. A high computational cost of BEM, however, has limited its application to relatively small scale problems. We have developed a graphics process unit (GPU) computing of BEM for capsules and biological cells in Stokes flow. We have investigated rheological properties of capsules, and those of capsule suspensions using the GPU-accelerated BEM. Here, we provide an overview of our recent studies, particularly focusing on the shear viscosity of dense suspensions of capsules in simple shear flow; an overshoot phenomenon of the capsule deformation in oscillating shear flow; and the sedimentation of red blood cells.
Yohsuke Imai, Daiki Matsunaga

Recent Advances in ALE-VMS and ST-VMS Computational Aerodynamic and FSI Analysis 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.
Artem Korobenko, Yuri Bazilevs, Kenji Takizawa, Tayfun E. Tezduyar

Space–Time Computational Analysis of Tire Aerodynamics with Actual Geometry, Road Contact, and Tire Deformation

A new space–time (ST) computational method, “ST-SI-TC-IGA,” is enabling us to address the challenges faced in computational analysis of tire aerodynamics with actual 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). 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 computation near the moving fluid–solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-SI enables high-resolution representation of the boundary layers near the tire. 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 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 surfaces 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, and one is a 3D model with an actual tire geometry that includes the longitudinal and transverse grooves. The computations show the effectiveness of the ST-SI-TC-IGA in tire aerodynamics.
Takashi Kuraishi, Kenji Takizawa, Tayfun E. Tezduyar

Thermal Convection in the van der Waals Fluid

In this work, the van der Waals fluid model, a diffuse-interface model for liquid–vapor two-phase flows, is numerically investigated. The thermodynamic properties of the van der Waals fluid are first studied. Dimensional analysis is performed to identify the control parameters for the system. An entropy-stable numerical scheme and isogeometric analysis are utilized to discretize the governing equations for numerical simulations. The steady state solution at low Rayleigh number is presented, demonstrating the capability of the model in describing liquid–vapor phase transitions. Next, two-dimensional nucleate and film boiling are simulated, showing the applicability of the model in different regimes of boiling. In the last, the heat transport property of the van der Waals model is numerically investigated. The scaling law for the Nusselt number with respect to the Rayleigh number in the van der Waals model is obtained by performing a suite of high-resolution simulations.
Ju Liu

A General-Purpose NURBS Mesh Generation Method for Complex Geometries

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.
Yuto Otoguro, Kenji Takizawa, Tayfun E. Tezduyar

Interface-Reproducing Capturing (IRC) Technique for Fluid-Structure Interaction: Methods and Applications

How to enhance the interface-capturing (IC) computation of fluid–structure interaction (FSI) is a long-standing issue for IC approaches. This chapter introduces approaches based on an extended finite element method (XFEM) and a Lagrange multiplier (LM) method, as well as our contribution to the problem. The XFEM-based approach develops a framework for an interface-reproducing capturing (IRC) method whose spatial functions are locally equivalent to those of interface-tracking (IT) methods. The XFEM enriches the velocity and pressure function spaces of the local flow around the interface. This enrichment reproduces requisite discontinuities at the interface. Simultaneously, the LM method imposes continuity on the fluid and structure to couple them, and thus the fluid captures the interface. This chapter gives an overview, describes the methods and solution techniques, and shows verifications and applications, focusing mainly on computing the fluid–thin-structure interaction (FTSI). The verifications reveal how continuity and discontinuity at the interface affect the FSI computation and why the IRC method is effective. Applications to flow-induced flutter of flexible thin objects show the ability of the proposed method to take on the challenge of computing complex FSI problems. Applications to flows past fixed objects show its ability to compute simple problems with ease. The IRC method therefore has two aspects and potentials. Open issues mentioned in this chapter indicate that there is still much room for advancing the IC method.
Tomohiro Sawada
Additional information

Premium Partner

image credits