Computational Fluid-Structure Interaction

Dr. Yuri Bazilevs received his PhD from University of Texas at Austin in 2006 and is an Associate Professor in Department of Structural Engineering at University of California, San Diego. He has been conducting computational fluid mechanics research since 2000, teaching classes on that subject since 2008, and has been conducting computational FSI research since 2005. He has published over 60 journal papers on computational fluid and structural mechanics and computational FSI. He coauthored a book on isogeometric analysis, a technique that is now widely used in computational fluid and structural mechanics and computational FSI. He taught short courses on these subjects. He received numerous awards for his research in computational fluid mechanics and FSI. He is an Assistant Editor of Springer journal Computational Mechanics for manuscripts on computational fluid mechanics and FSI. More information on Dr. Bazilevs can be found at ristretto.ucsd.edu/~bazily/.Dr. Kenji Takizawa received his PhD from Tokyo Institute of Technology in 2005 and is an Associate Professor in Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study at Waseda University, Tokyo. He has been conducting computational fluid mechanics research since 2000, teaching classes on that subject since 2010, and has been conducting computational FSI research since 2003. He has published over 80 papers on computational fluid mechanics and FSI, including 34 journal papers. He taught short courses on these subjects. He received numerous awards for his research in computational fluid mechanics and FSI. He is an Associate Editor of ASME Journal of Applied Mechanics and is responsible for manuscripts on computational fluid mechanics and FSI. He is also an Assistant Editor of Springer journal Computational Mechanics for manuscripts on computational fluid mechanics and FSI. More information on Dr. Takizawa can be found at jp.tafsm.org/.Dr. Tayfun Tezduyar received his PhD from Caltech in 1982 and is the James F. Barbour Professor in Mechanical Engineering at Rice University, Houston. He has been conducting computational fluid mechanics research since 1979, teaching classes on that subject since 1987, and has been conducting computational FSI research since 1991. He has published over 440 papers on computational fluid mechanics and FSI, including 200 journal papers. He taught short courses on these subjects. He received numerous awards for his research in computational fluid mechanics and FSI. He is an Editor of Springer journal Computational Mechanics and is responsible for the manuscripts on computational fluid mechanics and FSI. He was the director of the Army High Performance Computing Research Center in 1994-1998, Chairman of Mechanical Engineering and Materials Science at Rice in 1999-2004, and Chairman of ASME Applied Mechanics Division in 2010-2011. More information on Dr. Tezduyar can be found at tafsm.org/tezduyar/.

• Series Preface xi Preface xiiiAcknowledgements xix1 Governing Equations of Fluid and Structural Mechanics 11.1 Governing Equations of Fluid Mechanics 11.1.1 Strong Form of the Navier–Stokes Equations of Incompressible Flows 11.1.2 Model Differential Equations 51.1.3 Nondimensional Equations and Numbers 61.1.4 Some Specific Boundary Conditions 71.1.5 Weak Form of the Navier–Stokes Equations 101.2 Governing Equations of Structural Mechanics 121.2.1 Kinematics 121.2.2 Principle of Virtual Work and Variational Formulation of Structural Mechanics 141.2.3 Conservation of Mass 151.2.4 Structural Mechanics Formulation in the Current Configuration 151.2.5 Structural Mechanics Formulation in the Reference Configuration 171.2.6 Additional Boundary Conditions of Practical Interest 181.2.7 Some Constitutive Models 191.2.8 Linearization of the Structural Mechanics Equations: Tangent Stiffness and Equations of Linear Elasticity 221.2.9 Thin Structures: Shell, Membrane, and Cable Models 251.3 Governing Equations of Fluid Mechanics in Moving Domains 311.3.1 Kinematics of ALE and Space–Time Descriptions 311.3.2 ALE Formulation of Fluid Mechanics 332 Basics of the Finite Element Method for Nonmoving-Domain Problems 372.1 An Abstract Variational Formulation for Steady Problems 372.2 FEM Applied to Steady Problems 382.3 Construction of Finite Element Basis Functions 422.3.1 Construction of Element Shape Functions 432.3.2 Finite Elements Based on Lagrange Interpolation Functions 462.3.3 Construction of Global Basis Functions 492.3.4 Element Matrices and Vectors and their Assembly into the Global Equation System 512.4 Finite Element Interpolation and Numerical Integration 532.4.1 Interpolation by Finite Elements 532.4.2 Numerical Integration 552.5 Examples of Finite Element Formulations 582.5.1 Galerkin Formulation of the Advection–Diffusion Equation 582.5.2 Stabilized Formulation of the Advection–Diffusion Equation 592.5.3 Galerkin Formulation of Linear Elastodynamics 622.6 Finite Element Formulation of the Navier–Stokes Equations 652.6.1 Standard Essential Boundary Conditions 652.6.2 Weakly Enforced Essential Boundary Conditions 703 Basics of the Isogeometric Analysis 733.1 B-Splines in 1D 743.2 NURBS Basis Functions, Curves, Surfaces, and Solids 753.3 h-, p-, and k-Refinement of NURBS Meshes 773.4 NURBS Analysis Framework 784 ALE and Space–Time Methods for Moving Boundaries and Interfaces 834.1 Interface-Tracking (Moving-Mesh) and Interface-Capturing (Nonmoving-Mesh) Techniques 834.2 Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) 844.3 ALE Methods 844.4 Space–Time Methods 864.5 Advection–Diffusion Equation 894.5.1 ALE Formulation 894.5.2 Space–Time Formulation 914.6 Navier–Stokes Equations 924.6.1 ALE Formulation 924.6.2 Generalized-α Time Integration of the ALE Equations 954.6.3 Space–Time Formulation 984.7 Mesh Moving Methods 1065 ALE and Space–Time Methods for FSI 1115.1 FSI Formulation at the Continuous Level 1115.2 ALE Formulation of FSI 1145.2.1 Spatially-Discretized ALE FSI Formulation with Matching Fluid and Structure Discretizations 1145.2.2 Generalized-α Time Integration of the ALE FSI Equations 1185.2.3 Predictor–Multicorrector Algorithm and Linearization of the ALE FSI Equations 1205.3 Space–Time Formulation of FSI 1235.3.1 Core Formulation 1235.3.2 Interface Projection Techniques for Nonmatching Fluid and Structure Interface Discretizations 1275.4 Advanced Mesh Update Techniques 1295.4.1 Solid-Extension Mesh Moving Technique (SEMMT) 1295.4.2 Move-Reconnect-Renode Mesh Update Method (MRRMUM) 1325.4.3 Pressure Clipping 1345.5 FSI Geometric Smoothing Technique (FSI-GST) 1366 Advanced FSI and Space–Time Techniques 1396.1 Solution of the Fully-Discretized Coupled FSI Equations 1396.1.1 Block-Iterative Coupling 1406.1.2 Quasi-Direct Coupling 1416.1.3 Direct Coupling 1426.2 Segregated Equation Solvers and Preconditioners 1446.2.1 Segregated Equation Solver for Nonlinear Systems (SESNS) 1446.2.2 Segregated Equation Solver for Linear Systems (SESLS) 1456.2.3 Segregated Equation Solver for Fluid–Structure Interactions (SESFSI) 1466.3 New-Generation Space–Time Formulations 1496.3.1 Mesh Representation 1506.3.2 Momentum Equation 1506.3.3 Incompressibility Constraint 1516.4 Time Representation 1516.4.1 Time Marching Problem 1516.4.2 Design of Temporal NURBS Basis Functions 1536.4.3 Approximation in Time 1546.4.4 An Example: Circular-Arc Motion 1546.5 Simple-Shape Deformation Model (SSDM) 1576.6 Mesh Update Techniques in the Space–Time Framework 1586.6.1 Mesh Computation and Representation 1586.6.2 Remeshing Technique 1586.7 Fluid Mechanics Computation with Temporal NURBS Mesh 1596.7.1 No-Slip Condition on a Prescribed Boundary 1596.7.2 Starting Condition 1606.8 The Surface-Edge-Node Contact Tracking (SENCT-FC) Technique 1636.8.1 Contact Detection and Node Sets 1646.8.2 Contact Force and Reaction Force 1656.8.3 Solving for the Contact Force 1677 General Applications and Examples of FSI Modeling 1717.1 2D Flow Past an Elastic Beam Attached to a Fixed, Rigid Block 1717.2 2D Flow Past an Airfoil Attached to a Torsion Spring 1747.3 Inflation of a Balloon 1757.4 Flow Through and Around a Windsock 1777.5 Aerodynamics of Flapping Wings 1817.5.1 Surface and Volume Meshes 1817.5.2 Flapping-Motion Representation 1857.5.3 Mesh Motion 1867.5.4 Fluid Mechanics Computation 1878 Cardiovascular FSI 1918.1 Special Techniques 1948.1.1 Mapping Technique for Inflow Boundaries 1948.1.2 Preconditioning Technique 1958.1.3 Calculation of Wall Shear Stress 1958.1.4 Calculation of Oscillatory Shear Index 1968.1.5 Boundary Condition Techniques for Inclined Inflow and Outflow Planes 1978.2 Blood Vessel Geometry, Variable Wall Thickness, Mesh Generation, and Estimated Zero-Pressure (EZP) Geometry 1988.2.1 Arterial-Surface Extraction from Medical Images 1988.2.2 Mesh Generation and EZP Arterial Geometry 1998.2.3 Blood Vessel Wall Thickness Reconstruction 2018.3 Blood Vessel Tissue Prestress 2038.3.1 Tissue Prestress Formulation 2038.3.2 Linearized Elasticity Operator 2048.4 Fluid and Structure Properties and Boundary Conditions 2058.4.1 Fluid and Structure Properties 2058.4.2 Boundary Conditions 2058.5 Simulation Sequence 2098.6 Sequentially-Coupled Arterial FSI (SCAFSI) Technique 2108.7 Multiscale Versions of the SCAFSI Technique 2138.8 Computations with the SSTFSI Technique 2158.8.1 Performance Tests for Structural Mechanics Meshes 2158.8.2 Multiscale SCAFSI Computations 2188.8.3 WSS Calculations with Refined Meshes 2228.8.4 Computations with New Surface Extraction, Mesh Generation, and Boundary Condition Techniques 2258.8.5 Computations with the New Techniques for the EZP Geometry, Wall Thickness, and Boundary-Layer Element Thickness 2308.9 Computations with the ALE FSI Technique 2338.9.1 Cerebral Aneurysms: Tissue Prestress 2368.9.2 Total Cavopulmonary Connection 2408.9.3 Left Ventricular Assist Device 2509 Parachute FSI 2599.1 Parachute Specific FSI-DGST 2619.2 Homogenized Modeling of Geometric Porosity (HMGP) 2629.2.1 HMGP in its Original Form 2659.2.2 HMGP-FG 2669.2.3 Periodic n-Gore Model 2679.3 Line Drag 2699.4 Starting Point for the FSI Computation 2719.5 “Symmetric FSI” Technique 2749.6 Multiscale SCFSI M2C Computations 2759.6.1 Structural Mechanics Solution for the Reefed Stage 2759.6.2 Fabric Stress Computations 2789.7 Single-Parachute Computations 2809.7.1 Various Canopy Configurations 2809.7.2 Various Suspension Line Length Ratios 2889.8 Cluster Computations 2939.8.1 Starting Conditions 2949.8.2 Computational Conditions 2959.8.3 Results 2979.9 Techniques for Dynamical Analysis and Model-Parameter Extraction 2999.9.1 Contributors to Parachute Descent Speed 2999.9.2 Added Mass 31110 Wind-Turbine Aerodynamics and FSI 31510.1 Aerodynamics Simulations of a 5MW Wind-Turbine Rotor 31710.1.1 5MW Wind-Turbine Rotor Geometry Definition 31710.1.2 ALE-VMS Simulations Using NURBS-based IGA 32210.1.3 Computations with the DSD/SST Formulation Using Finite Elements 32510.2 NREL Phase VI Wind-Turbine Rotor: Validation and the Role of Weakly-Enforced Essential Boundary Conditions 32810.3 Structural Mechanics of Wind-Turbine Blades 33410.3.1 The Bending-Strip Method 33410.3.2 Time Integration of the Structural Mechanics Equations 34010.4 FSI Coupling and Aerodynamics Mesh Update 34210.5 FSI Simulations of a 5MW Wind-Turbine Rotor 34310.6 Pre-Bending of the Wind-Turbine Blades 34410.6.1 Problem Statement and the Pre-Bending Algorithm 34610.6.2 Pre-Bending Results for the NREL 5MW Wind-Turbine Blade 349References 353Index 373

“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.”  (Expofairs, 18 October 2013)