Handbook of Numerical Analysis IX
1st Edition
Published on 25. July 2003
1187 pages
978-0-08-050794-1 (ISBN)
Description
Numerical Methods for Fluids, Part 3
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Language
English
Place of publication
Oxford
United States
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Windows
File size
18,52 MB
ISBN-13
978-0-08-050794-1 (9780080507941)
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P.G. Ciarlet
Numerical Methods for Fluids, Part 3: Volume 9
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07/2003
Elsevier
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Content
- Front Cover
- Numerical Methods for Fluids (Part 3)
- Copyright Page
- Contents
- Preface
- Chapter I. The Navier-Stokes Equations for Incompressible Viscous Fluids
- Introduction: Synopsis
- 1. Derivation of the Navier-Stokes equations for viscous fluids
- 2. Initial and boundary conditions
- 3. A stream function-vorticity formulation of the Navier-Stokes equations
- 4. A brief introduction to Sobolev spaces
- 5. Variational formulations of the Navier-Stokes equations
- 6. A short review of mathematical results for the Navier-Stokes equations
- Chapter II. A Family of Operator-Splitting Methods for Initial Value Problems. Application to the Navier-Stokes Equationsh
- Introduction: Synopsis
- 7. A family of initial value problems
- 8. The Peaceman-Rachford method
- 9. The Douglas-Rachford method
- 10. A ? -scheme
- 11. Application to the Navier-Stokes equations
- 12. Further comments
- Chapter III. Iterative Solution of the Advection-Diffusion Subproblems
- Introduction: Synopsis
- 13. Classical and variational formulations of the advection-diffusion subproblems associated with the operator splitting schemes
- 14. Linear variational problems in Hilbert spaces
- 15. Variational methods for the solution of the advection-diffusion problems (13.1) and (13.2)
- 16. Conjugate gradient methods for the solution of minimization problems in Hilbert spaces
- 17. Least squares solution of linear and nonlinear problems in Hilbert spaces
- 18. Least-squares/conjugate gradient solution of problems (13.1) and (13.2)
- Chapter IV. Iterative Solution of the Stokes Subproblems
- Introduction: Synopsis
- 19. Mathematical properties of the generalized Stokes problem (GS)1
- 20. Gradient methods for the Stokes problem
- 21. Conjugate gradient methods for the Stokes problem (GS)1
- 22. Iterative solution of the generalized Stokes problem (GS)2
- 23. On artificial compressibility methods and further comments
- Chapter V. Finite Element Approximation of the Navier-Stokes Equations
- Introduction: Synopsis
- 24. Solution of the Stokes problem with periodic boundary conditions
- 25. A Fourier analysis of the numerical instability mechanism
- 26. Finite element methods for the Stokes problem
- 27. Finite element implementation of the ? -scheme (11.5)-(11.8)
- 28. On the numerical solution of the discrete subproblems
- 29. Further comments and complements
- Chapter VI. Treatment of the Advection by a Wave-Like Equation Method and by Backward Methods of Characteristics
- Introduction: Synopsis
- 30. More on operator-splitting methods
- 31. A wave-like equation method for solving the Navier-Stokes equations
- 32. Solution of the Navier-Stokes equations by backward methods of characteristics
- 33. On the treatment of the advection by upwinding. Final comments
- Chapter VII. On L2-Projection Methods for the Numerical Treatment of the Incompressibility
- Introduction: Synopsis
- 34. Combining L2-projection methods with operator-splitting schemes à la Peaceman-Rachford and Douglas-Rachford, and with the theta-scheme
- 35. Combining L2-projection methods with operator-splitting schemes à la Marchuk-Yanenko
- 36. Numerical experiments
- 37. Further comments and references
- Chapter VIII. Fictitious Domain Methods for Incompressible Viscous Flow: Application to Particulate Flow
- Introduction: Synopsis
- 38. Generalities on fictitious domain methods
- 39. On the solution of Dirichlet problems by fictitious domain methods with boundary supported Lagrange multipliers. Applications to the solution of some nonlinear Dirichlet problems
- 40. A boundary supported Lagrange multiplier/fictitious domain method for the incompressible Navier-Stokes equations
- 41. On a fictitious domain method with volume distributed Lagrange multipliers for Dirichlet problems
- 42. On the direct numerical simulation of incompressible viscous flow with moving rigid boundary by distributed Lagrange multiplier based fictitious domain methods. Application to particulate flow
- Chapter IX. Numerical Experiments
- Introduction: Synopsis
- 43. Flow in a nozzle at high incidence
- 44. Application of the wave-like equation method to the numerical simulation of incompressible viscous fluid flow in square and cubic cavities
- 45. Numerical simulation of incompressible viscous flow a two-dimensional channel with a backward facing step
- 46. Numerical simulation of a thermal convection flow in a differentially-heated rectangular cavity
- 47. More on particulate flow
- 48. On blood flow in the heart
- Chapter X. Complements: From Stream Function-Vorticity to Flow Control
- Introduction: Synopsis
- 49. Numerical methods for the stream function-vorticity formulation of the Navier-Stokes equations
- 50. Simulation of Bingham visco-plastic flow
- 51. On the numerical simulation of slightly compressible isentropic viscous flow
- 52. Modeling and simulation of low-Mach-number compressible flows
- 53. Optimal control of systems modeled by the incompressibleNavier-Stokes equations: Drag reduction by active control for flow past cylinders
- Acknowledgements
- References
- Author Index
- Subject Index
