Mesh Adaptation for Computational Fluid Dynamics, Volume 2 - Unsteady and Goal-oriented Adaptation

Simulation technology, and computational fluid dynamics (CFD) in particular, is essential in the search for solutions to the modern challenges faced by humanity. Revolutions in CFD over the last decade include the use of unstructured meshes, permitting the modeling of any 3D geometry. New frontiers point to mesh adaptation, allowing not only seamless meshing (for the engineer) but also simulation certification for safer products and risk prediction.
 
Mesh Adaptation for Computational Dynamics 2 is the second of two volumes and introduces topics including optimal control formulation, minimizing a goal function, and extending the steady algorithm to unsteady physics. Also covered are multi-rate strategies, steady inviscid flows in aeronautics and an extension to viscous flows.
 
This book will be useful to anybody interested in mesh adaptation pertaining to CFD, especially researchers, teachers and students.

Sommario

Acknowledgments ix
 
Introduction xi
 
Chapter 1 Nonlinear Corrector for CFD 1
 
1.1. Introduction 1
 
1.1.1. Linear correction 3
 
1.1.2. Nonlinear correction 4
 
1.2. Two correctors for the Poisson problem 5
 
1.2.1. Notations 5
 
1.2.2. A priori corrector for the PDE solution 6
 
1.2.3. Finer-grid DC corrector for the PDE solution 8
 
1.3. RANS equations 9
 
1.3.1. Vector form of the RANS system 9
 
1.3.2. Formal discretization 10
 
1.3.3. Notations for discretization 11
 
1.4. Nonlinear functional correction 13
 
1.4.1. Finite volume nonlinear corrector 13
 
1.4.2. Finite element corrector 15
 
1.5. Example: supersonic flow 17
 
1.6. Concluding remarks 18
 
1.7. Notes 20
 
Chapter 2 Multi-scale Adaptation for Unsteady Flows 21
 
2.1. Introduction 21
 
2.2. Mesh adaptation efficiency 23
 
2.2.1. Regular and singular unsteady model 23
 
2.2.2. Representativity of the spatial interpolation error 24
 
2.3. Transient fixed-point mesh adaptation scheme 25
 
2.3.1. Size of subintervals in a mesh convergence 28
 
2.3.2. Mesh adaptation for unsteady Euler/Navier-Stokes equations with thickened interface 29
 
2.3.3. Convergent transient fixed-point 33
 
2.4. 2D bi-fluid example 33
 
2.5. Example: impact of a 3D water column on a obstacle 35
 
2.6. Conclusion 39
 
2.7. Appendix: remarks about the adaptation of the time step 39
 
2.8. Notes 41
 
Chapter 3 Multi-rate Time Advancing 43
 
3.1. Introduction 43
 
3.2. Multi-rate time advancing by volume agglomeration 45
 
3.2.1. Finite volume Navier-Stokes 45
 
3.2.2. Inner and outer zones 46
 
3.2.3. MR time advancing 47
 
3.3. Elements of analysis 49
 
3.3.1. Stability 49
 
3.3.2. Accuracy 50
 
3.3.3. Efficiency 51
 
3.3.4. Toward many rates 52
 
3.3.5. Impact of our MR complexity on mesh adaption 52
 
3.3.6. Parallelism 53
 
3.4. Applications 55
 
3.4.1. Circular cylinder at very high Reynolds number 55
 
3.4.2. Mesh adaption for a contact discontinuity 58
 
3.5. Conclusion 59
 
3.6. Notes 60
 
Chapter 4 Goal-Oriented Adaptation for Inviscid Steady Flows 65
 
4.1. Introduction 65
 
4.1.1. What to do with this estimate? 67
 
4.1.2. Adjoint-L 1 approach 68
 
4.1.3. Outline 69
 
4.2. A more accurate nonlinear error analysis 69
 
4.2.1. Assumptions and definitions 69
 
4.2.2. A priori estimation 70
 
4.3. The case of the steady Euler equations 72
 
4.3.1. Variational analysis 72
 
4.3.2. Approximation error estimation 73
 
4.4. Error model minimization 74
 
4.5. Adaptative strategy 76
 
4.5.1. Adjoint solver 77
 
4.5.2. Optimal goal-oriented discrete metric 77
 
4.5.3. Controlled mesh regeneration 79
 
4.6. Numerical outputs 79
 
4.6.1. High-fidelity pressure prediction of an aircraft 79
 
4.7. Conclusion 82
 
4.8. Notes 82
 
Chapter 5. Goal-Oriented Adaptation for Viscous Steady Flows 85
 
5.1. Introduction 85
 
5.2. Case of an elliptic problem 86
 
5.2.1. A priori finite-element analysis (first estimate) 86
 
5.2.2. Goal-oriented adaptation according to lemma 5.1 89
 
5.2.3. Goal-oriented adaptation according to a second estimate 91
 
5.3. Error analysis for Navier-Stokes problem 92
 
5.3.1. Mesh adaptation problem statement 92
 

Info autore

Alain Dervieux is chief scientist at the Société Lemma and emeritus senior scientist at Inria, Sophia Antipolis. His main research interests are computational fluid dynamics, particularly approximations on unstructured meshes.

Frederic Alauzet is a senior researcher at Inria Saclay and adjunct professor at Mississippi State University. His research focuses on anisotropic mesh adaptation, advanced solvers, mesh generation and moving mesh methods.

Adrien Loseille is a research scientist at Inria Saclay, working in Luminary Cloud. His main domains of interest are unstructured mesh generation and adaptation for computational fluid dynamics.

Bruno Koobus is professor at the University of Montpellier. His main research interests cover computational fluid dynamics, in particular the development of numerical methods on fixed and moving meshes, turbulence modeling and parallel algorithms.

Riassunto

Simulation technology, and computational fluid dynamics (CFD) in particular, is essential in the search for solutions to the modern challenges faced by humanity. Revolutions in CFD over the last decade include the use of unstructured meshes, permitting the modeling of any 3D geometry. New frontiers point to mesh adaptation, allowing not only seamless meshing (for the engineer) but also simulation certification for safer products and risk prediction.

Mesh Adaptation for Computational Dynamics 2 is the second of two volumes and introduces topics including optimal control formulation, minimizing a goal function, and extending the steady algorithm to unsteady physics. Also covered are multi-rate strategies, steady inviscid flows in aeronautics and an extension to viscous flows.

This book will be useful to anybody interested in mesh adaptation pertaining to CFD, especially researchers, teachers and students.

Dettagli sul prodotto

• Autori: Frederic Alauzet, DERVIEUX, Alain Dervieux, Bruno Koobus, Adrien Loseille
• Editore: Wiley & Sons
• Lingue: Inglese
• Formato: Copertina rigida
• Pubblicazione: 14.11.2022
• EAN: 9781786308320
• ISBN: 978-1-78630-832-0
• Pagine: 240
• Dimensioni: 156 mm x 235 mm x 14 mm
• Peso: 447 g
• Categorie: Scienze naturali, medicina, informatica, tecnica > Fisica, astronomia > Tematiche generali, enciclopedie; Physik, Maschinenbau, Mathematische Physik, Strömungsmechanik, Physics, Mechanical Engineering, Fluid mechanics, Computational / Numerical Methods, Rechnergestützte / Numerische Verfahren im Maschinenbau, Mathematical & Computational Physics