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4 Time-integration

  • Bernard J. Geurts
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Direct and Large-Eddy Simulation
This chapter is in the book Direct and Large-Eddy Simulation

Abstract

We describe explicit and implicit time-stepping methods that can be used to efficiently simulate the evolution of turbulent flow. The stability time step restrictions and order of accuracy of explicit Runge-Kutta methods will be considered in some detail. Moreover, basic implicit methods will be introduced as well as methods to solve linear systems of equations arising as part of their formulation. The problem of determining a suitable time-step consistent with a certain desired temporal accuracy will be discussed.

Abstract

We describe explicit and implicit time-stepping methods that can be used to efficiently simulate the evolution of turbulent flow. The stability time step restrictions and order of accuracy of explicit Runge-Kutta methods will be considered in some detail. Moreover, basic implicit methods will be introduced as well as methods to solve linear systems of equations arising as part of their formulation. The problem of determining a suitable time-step consistent with a certain desired temporal accuracy will be discussed.

Chapters in this book

  1. Frontmatter I
  2. Preface VII
  3. Contents IX
  4. Part I: Phenomenology of turbulent flow
  5. 1 Direct and large-eddy simulation: context and introduction 1
  6. 2 Computational dynamical systems for turbulence 38
  7. Part II: Numerical aspects of DNS and LES
  8. 3 Features of a basic numerical approach 65
  9. 4 Time-integration 87
  10. 5 Spatial discretization 110
  11. Part III: Subgrid modeling
  12. 6 Filtering and rigorous subgrid modeling 165
  13. 7 Subgrid models 200
  14. Part IV: Validation and error-assessment
  15. 8 Validation of large-eddy simulation 235
  16. 9 Interacting error dynamics 258
  17. 10 Epilogue 289
  18. Bibliography 295
  19. Index 305
https://doi.org/10.1515/9783110532364-004

Chapters in this book

  1. Frontmatter I
  2. Preface VII
  3. Contents IX
  4. Part I: Phenomenology of turbulent flow
  5. 1 Direct and large-eddy simulation: context and introduction 1
  6. 2 Computational dynamical systems for turbulence 38
  7. Part II: Numerical aspects of DNS and LES
  8. 3 Features of a basic numerical approach 65
  9. 4 Time-integration 87
  10. 5 Spatial discretization 110
  11. Part III: Subgrid modeling
  12. 6 Filtering and rigorous subgrid modeling 165
  13. 7 Subgrid models 200
  14. Part IV: Validation and error-assessment
  15. 8 Validation of large-eddy simulation 235
  16. 9 Interacting error dynamics 258
  17. 10 Epilogue 289
  18. Bibliography 295
  19. Index 305
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