Arbitrary Lagrangian Eulerian and Fluid-Structure Interaction: Numerical Simulation

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