Mesh optimization step

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Table of contents

Introduction 
I 3D FSI moving mesh simulations
Introduction
1 Connectivity-change moving mesh strategy 
1.1 Our moving mesh algorithm
1.1.1 A two step process
1.1.2 Mesh deformation step
1.1.3 Mesh optimization step
1.1.4 Optimization procedure
1.1.5 Handling of boundaries
1.1.6 Algorithm
1.1.7 Choice of the di↵erent parameters for a robust algorithm
1.2 Mesh deformation with Inverse Distance Weighted method
1.2.1 IDW method
1.2.2 Implementation
1.3 Examples
1.3.1 Rigid-body examples
1.3.2 Deformable-body examples
1.4 Boundary layers for deformable geometries
1.4.1 One boundary layer
1.4.2 Several boundary layers
1.5 Large volume variations
1.5.1 Engine piston
1.6 Conclusion
2 ALE solver 
2.1 Euler equations in the ALE framework
2.2 Spatial discretization
2.2.1 Edge-based Finite-Volume solver
2.2.2 HLLC numerical flux
2.2.3 High-order scheme
2.2.4 Limiter
2.2.5 Boundary conditions
2.3 Time discretization
2.3.1 The Geometric Conservation Law
2.3.2 Discrete GCL enforcement
2.3.3 RK schemes
2.3.4 Application to the SSPRK(4,3) scheme
2.3.5 Practical computation of the volumes swept
2.3.6 MUSCL approach and RK schemes
2.3.7 Computation of the time step
2.3.8 Handling the swaps
2.4 FSI coupling
2.4.1 Movement of the geometries
2.4.2 Discretization
2.4.3 Explicit coupling
2.5 Implementation
2.5.1 Non-dimensionalization
2.5.2 Parallelization
2.6 Conclusion
3 Numerical Examples 
3.1 Validation of the solver
3.1.1 Static vortex in a rotating mesh
3.1.2 Flat plate in free fall
3.1.3 Piston
3.2 Numerical examples
3.2.1 AGARD test cases
3.2.2 F117 nosing up
3.2.3 Two F117 aircraft crossing flight paths
3.2.4 Ejected cabin door
3.3 Parallel performance
3.4 Conclusion
Conclusion
II Extension of anisotropic metric-based mesh adaptation to moving mesh simulations 
Introduction
4 Basics of metric based mesh adaptation 
4.1 State of the art
4.1.1 Meshing status
4.1.2 History of metric-based mesh adaptation
4.1.3 Other mesh adaptation approaches
4.2 Principle of metric-based adaptation
4.2.1 Euclidian and Riemannian metric spaces
4.2.2 Unit mesh
4.2.3 Operations on metrics
4.2.4 The non-linear adaptation loop
4.3 The continuous mesh framework
4.3.1 Duality discrete-continous: a new formalism
4.3.2 Continuous linear interpolation
4.3.3 Summary
4.4 Multiscale mesh adaptation
4.4.1 Optimal control of the interpolation error and optimal meshes
4.4.2 Control of the error in Lp norm
4.5 Conclusion
5 Unsteady mesh adaptation 
5.1 Error estimate
5.1.1 Error model
5.1.2 Spatial minimization for a fixed t
5.1.3 Temporal minimization
5.1.4 Error analysis for time sub-intervals
5.1.5 Global fixed-point mesh adaptation algorithm
5.2 From theory to practice
5.2.1 Computation of the mean Hessian-metric
5.2.2 Choice of the optimal continuous mesh
5.2.3 Matrix-free P1-exact conservative solution transfer
5.2.4 The remeshing step
5.2.5 Software used
5.3 Choice of the mean Hessian-metric
5.4 Numerical examples
5.4.1 2D shock-bubble interaction
5.4.2 3D circular blast
5.4.3 3D shock-bubble interaction
5.4.4 3D blast on the London Tower Bridge
5.5 Parallelization of the mesh adaptation loop
5.5.1 Choices of implementation
5.5.2 Analysis of parallel timings
5.5.3 Conclusion
5.6 Conclusion
6 Extension of unsteady adaptation to moving meshes 
6.1 ALE metric
6.2 Analytic examples
6.2.1 Procedure
6.2.2 Functions considered
6.2.3 Results
6.3 Update of the adaptation algorithm
vi Contents
6.3.1 Error analysis
6.3.2 Algorithm
6.3.3 Update of the metric for optimizations
6.3.4 Handling of the surface
6.4 3D numerical examples
6.4.1 Shock tube in expansion
6.4.2 Moving ball in a shock tube
6.4.3 Nosing-up f117
6.4.4 Two F117 aircraft flight paths crossing
6.5 Conclusion
Conclusion
Conclusion and perspectives 
Acknowledgments
Appendices