Arbitrary Lagrangian Eulerian and Fluid-Structure Interaction (eBook)

Mhamed Souli is Professor of computational mechanics at Lille University in France. His research and development interests include fluid structure interaction, CFD with emphasis on multiphase flow and coupling with structures, and their applications to industrial problems. David J. Benson is Professor of Computational Mechanics in the Department of Structural Engineering at the University of California, San Diego. He is a Fellow of the American Physical Society, American Society of Mechanical Engineers, and the US Association of Computational Mechanics. He serves on the editorial board of the International Journal of Solids and Structures.

Introduction xi

Mhamed SOULI

Chapter 1. Introduction to Arbitrary
Lagrangian-Eulerian in Finite Element Methods 1

David J. BENSON

1.1. Introduction 1

1.2. Governing equations 3

1.3. Operator splitting 4

1.4. The Lagrangian step 7

1.5. Mesh relaxation 25

1.6. The Eulerian step 27

1.7. Future research directions 44

1.8. Bibliography 45

Application to Dynamic Problems 51

Mhamed SOULI

2.1. Introduction 51

2.2. General ALE description of Navier-Stokes equations
54

2.3. Fluid-structure interaction 57

2.4. Numerical applications 72

Chapter 2. Fluid-Structure Interaction: Application to
Dynamic Problems 51

Mhamed SOULI

2.5. Conclusion 104

2.6. Acknowledgments 104

2.7. Bibliography 105

Chapter 3. Implicit Partitioned Coupling in
Fluid-Structure Interaction 109

Michael SCHÄFER

3.1. Introduction 109

3.2. Computational fluid mechanics 110

3.3. Computational structural mechanics 121

3.4. Fluid-structure interaction algorithms 136

3.5. Results and applications 150

3.6. Bibliography 161

Chapter 4. Avoiding Instabilities Caused by Added Mass
Effects in Fluid-Structure Interaction Problems
165

Sergio IDELSOHN, Facundo DEL PIN and Riccardo ROSSI

4.1. Introduction 165

4.2. The discretized equations to be solved in a FSI problem
169

4.3. Monolithic solution of the FSI equations by pressure
segregation 174

4.4. Static condensation of the pressure 176

4.5. Evaluation of the Laplace matrix for FSI problems 187

4.6. The partitioned (or staggered) scheme 189

4.7. Numerical examples 195

4.8. Conclusions 215

4.9. Acknowledgments 216

4.10. Bibliography 216

Chapter 5. Multidomain Finite Element Computations:
Application to Multiphasic Problems 221

Thierry COUPEZ, Hugues DIGONNET, Elie HACHEM, Patrice LAURE, Luisa
SILVA, Rudy VALETTE

5.1. Introduction 221

5.2. Characterization of different phases 228

5.3. Stabilized finite element formulations 240

5.4. Multiphasic problems with fluid-air and
fluid-fluid interface 256

5.5. Immersion of solid bodies in fluid 264

5.6. Conclusion 281

5.7. Acknowledgements 282

5.8. Bibliography 282

List of Authors 291

Index 293