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3 Features of a basic numerical approach

  • Bernard J. Geurts
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Direct and Large-Eddy Simulation
Ein Kapitel aus dem Buch Direct and Large-Eddy Simulation

Abstract

We formulate the basic numerical approach to simulate the Navier-Stokes equations, both for compressible as well as incompressible fluids. We present two different numerical representations of the solution that both give rise to large systems of ordinary differential equations. In particular, we consider the method of lines to obtain a discretization that can directly comply with the main conservation properties of the Navier-Stokes equations. Moreover, we consider finite element discretization. We also describe and illustrate the main aspects that influence the quality of a numerical solution, such as the order of accuracy of the scheme, stability and convergence. Finally, we turn to computational characteristics of the discrete problem and present global templates within which compressible and incompressible flow solvers can be formulated.

Abstract

We formulate the basic numerical approach to simulate the Navier-Stokes equations, both for compressible as well as incompressible fluids. We present two different numerical representations of the solution that both give rise to large systems of ordinary differential equations. In particular, we consider the method of lines to obtain a discretization that can directly comply with the main conservation properties of the Navier-Stokes equations. Moreover, we consider finite element discretization. We also describe and illustrate the main aspects that influence the quality of a numerical solution, such as the order of accuracy of the scheme, stability and convergence. Finally, we turn to computational characteristics of the discrete problem and present global templates within which compressible and incompressible flow solvers can be formulated.

Kapitel in diesem Buch

  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/10.1515/9783110532364-003

Kapitel in diesem Buch

  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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Heruntergeladen am 1.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/9783110532364-003/html
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