Computational Mechanics of Fluid-Structure Interaction: Computational Methods for Coupled Fluid-Structure Analysis

Preface I
Preface II
Acknowledgements
Contents
1 Introduction: A Computational Approach
	1.1 Some Motivating Applications and Challenges
		1.1.1 Marine and Offshore Engineering
		1.1.2 Energy Harvesting via Flow-Induced Vibration
		1.1.3 Bio-Inspired Drones and Unmanned Air Vehicles
		1.1.4 Flow-Induced Vibration and Control
	1.2 Continuum Mechanics Aspects of Fluid-Structure Interaction
		1.2.1 Interface Conditions
		1.2.2 Coordinate Frames and Motion of Continuum Domains
		1.2.3 Solution of Coupled Partial Differential Equations
	1.3 Book Organization
2 Equilibrium, Kinematics and Balance Laws
	2.1 Mechanical Forces and Equilibrium
		2.1.1 Body Forces
		2.1.2 Surface Forces
		2.1.3 Equilibrium
	2.2 Kinematics
		2.2.1 Configurations and Deformations
		2.2.2 Deformation Map
	2.3 Motion Kinematics
		2.3.1 Spatial or Coordinate Derivatives
		2.3.2 Time Derivatives
		2.3.3 Velocity and Acceleration Fields
	2.4 Rate of Strain
	2.5 Rigid Body Motions
		2.5.1 Geometric Description of Rotation
		2.5.2 Parameterization of Rotation Matrix
	2.6 Change of Variables
		2.6.1 Transformation of Volume Integrals
		2.6.2 Transformation of Surface Integrals
	2.7 Balance Laws in Lagrangian Form
		2.7.1 Conservation of Mass
		2.7.2 Conservation of Linear Momentum
		2.7.3 Application to Deformable Solid Models
	2.8 Balance Laws in Eulerian Form
		2.8.1 Conservation of Mass
		2.8.2 Conservation of Linear Momentum
		2.8.3 Application to Fluid Models
3 Fluid-Structure Equations with Body-Fitted Interface
	3.1 Continuum Mechanics of Fluid and Solid
		3.1.1 Lagrangian Solid System
		3.1.2 Eulerian Fluid System
	3.2 Kinematics of Eulerian and Lagrangian Modeling
		3.2.1 Deformation Mapping
	3.3 Continuum Mechanics of Moving Domains
		3.3.1 Arbitrary Lagrangian Eulerian Description
	3.4 Coupled Fluid-Structure Equations
		3.4.1 Coordinate System
		3.4.2 Coupled Formulation
		3.4.3 ALE Formulation
		3.4.4 Boundary and Initial Conditions
	3.5 Application of ALE Formulation for FSI Equations
4 Variational and Stabilized Finite Element Methods
	4.1 Introduction
	4.2 The Convection-Diffusion-Reaction Equation
		4.2.1 Strong Differential Form
		4.2.2 Semi-Discrete Variational Form
	4.3 The Positivity Preserving Variational (PPV) Method
		4.3.1 Linear Stabilization
		4.3.2 Positivity and Nonlinear Stabilization
	4.4 Convergence and Stability Analysis
		4.4.1 Dependence of Error on the Non-Dimensional Parameters
		4.4.2 One- and Two-Dimensional Fourier Analysis
		4.4.3 Mesh Convergence Study
	4.5 Numerical Results
		4.5.1 One-Dimensional Cases
		4.5.2 Two-Dimensional Cases
		4.5.3 Non-Uniform Unstructured and Anisotropic Meshes
5 Fluid-Structure Interaction: Variational Formulation
	5.1 Introduction
	5.2 Weak Variational Form for Fluid-Structure Interaction
		5.2.1 Trial and Test Function Spaces
		5.2.2 Weak Formulation for FSI
	5.3 Semi-Discrete Temporal Discretization
		5.3.1 Generalized-α Time Integration
		5.3.2 Semi-Discrete Temporal Discretization Applied to FSI
	5.4 Finite Element Space Discretization for FSI
	5.5 Matrix Form of the Linear System of Equations
	5.6 Solution Procedure
		5.6.1 Monolithic Solution for FSI
		5.6.2 Partitioned Solution for FSI
	Appendix
6 Quasi-Monolithic Fluid-Structure Formulation
	6.1 Introduction
	6.2 Weak Variational Form
		6.2.1 Combined Fluid-Structure Formulation
		6.2.2 Finite Element Space Discretization
	6.3 Quasi-Monolithic Formulation
		6.3.1 Second-Order in Time Discretization
		6.3.2 Complete Scheme
		6.3.3 Algorithm
	6.4 Extension to Multiple Flexible-Bodies
	6.5 Fully Stabilized Quasi-Monolithic Formulation
		6.5.1 Algorithm
	6.6 Parallel Implementation
	6.7 Convergence and Verification
		6.7.1 Numerical Assessment of Temporal Accuracy
		6.7.2 Verification of 2D and 3D FSI Frameworks
		6.7.3 Verification for Flapping Dynamics
7 Partitioned Fluid-Structure Interaction Methods
	7.1 Introduction
	7.2 Spatial Coupling Techniques
		7.2.1 Point-to-Point Mapping
		7.2.2 Point-to-Element Projection
		7.2.3 Common-Refinement Projection
	7.3 Temporal Coupling Techniques
		7.3.1 Staggered Loosely Coupled Techniques
		7.3.2 Strongly Coupled Techniques
	7.4 Common-Refinement Projection with Nonlinear Iterative Force Correction
		7.4.1 Error Analysis and Convergence Study
		7.4.2 Three-Dimensional FSI with Non-Matching Meshes
		7.4.3 Application to Offshore Riser VIV
8 Two-Phase Fluid-Structure Interaction
	8.1 Introduction
	8.2 Governing Equations for Two-Phase Flow
		8.2.1 The Navier-Stokes Equations
		8.2.2 The Fluid-Fluid Interface
		8.2.3 The Allen-Cahn Equation
	8.3 Partitioned Iterative Coupling
		8.3.1 Two-Phase Flow System
		8.3.2 Two-Phase Fluid-Structure Interaction System
		8.3.3 General Remarks
	8.4 Numerical Tests
		8.4.1 Verification of the Allen-Cahn Implementation
		8.4.2 Two-Phase Flow Coupling
		8.4.3 Two-Phase Fluid-Structure Interaction Coupling
	8.5 Application to Wave-Structure Interaction
	8.6 Application to Flexible Riser FSI with Internal Two-Phase Flow
		8.6.1 Amplitude Response and Flow Patterns
		8.6.2 Relationship Between VIV and Internal Flow Patterns
	8.7 Interface-Capturing via Mesh Adaptivity
9 Flexible Multibody Fluid-Structure Interaction
	9.1 Introduction
	9.2 Three-Dimensional Flexible Multibody Structural Framework
		9.2.1 Co-Rotational Multibody Structural Framework for Small Strain Problems
		9.2.2 Constraints for Joints Connecting Multiple Bodies
	9.3 Variational Formulation for the Flexible Multibody Framework
	9.4 Fluid-Structure Coupling Based on Line-to-Surface and Surface-to-Line Mapping
		9.4.1 Line-to-Surface Coupling
		9.4.2 Surface-to-Line Coupling
		9.4.3 Implementation Details
		9.4.4 Validation of Vortex-Induced Vibration of Flexible Cylinder
		9.4.5 Application to Coupled Floater-Mooring-Riser System
	9.5 Fluid-Structure Coupling Based on Radial Basis Function Mapping
		9.5.1 Convergence and Validation Tests: Flow Across a Pitching Plate
		9.5.2 Flow Across a Flexible Flapping Wing
		9.5.3 Three-Dimensional Flapping Dynamics of a Bat at Re=12,000
10 Turbulence Modeling in Fluid-Structure Interaction
	10.1 Introduction
	10.2 Dynamic Subgrid-Scale Model
		10.2.1 Stationary and Vibrating Square Cylinder at Moderate Reynolds Number
		10.2.2 Application to Semi-Submersible Floater
	10.3 Spalart-Allmaras Based Delayed Detached Eddy Simulation
		10.3.1 Formulation
		10.3.2 Flow Across Circular Cylinder at Re =3900  and Re = 140,000
		10.3.3 Application to VIV of an Offshore Riser
Appendix  References