HANDBOOK OF NUMERICAL ANALYSIS IX
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Table of contents
- Cover
- Contents5
- Preface9
- Chapter I. The Navier–Stokes Equations for Incompressible Viscous Fluids13
- Introduction: Synopsis13
- 1. Derivation of the Navier–Stokes equations for viscous fluids13
- 2. Initial and boundary conditions21
- 3. A stream function-vorticity formulation of the Navier–Stokes equations23
- 4. A brief introduction to Sobolev spaces27
- 5. Variational formulations of the Navier–Stokes equations34
- 6. A short review of mathematical results for the Navier–Stokes equations48
- Chapter II. A Family of Operator-Splitting Methods for Initial Value Problems. Application to the Na51
- Introduction: Synopsis51
- 7. A family of initial value problems52
- 8. The Peaceman–Rachford method52
- 9. The Douglas–Rachford method60
- 10. A θ -scheme63
- 11. Application to the Navier–Stokes equations71
- 12. Further comments73
- Chapter III. Iterative Solution of the Advection-Diffusion Subproblems77
- Introduction: Synopsis77
- 13. Classical and variational formulations of the advection-diffusion subproblems associated with th78
- 14. Linear variational problems in Hilbert spaces80
- 15. Variational methods for the solution of the advection-diffusion problems (13.1) and (13.2)102
- 16. Conjugate gradient methods for the solution of minimization problems in Hilbert spaces123
- 17. Least squares solution of linear and nonlinear problems in Hilbert spaces143
- 18. Least-squares/conjugate gradient solution of problems (13.1) and (13.2)181
- Chapter IV. Iterative Solution of the Stokes Subproblems189
- Introduction: Synopsis189
- 19. Mathematical properties of the generalized Stokes problem (GS)1190
- 20. Gradient methods for the Stokes problem218
- 21. Conjugate gradient methods for the Stokes problem (GS)1247
- 22. Iterative solution of the generalized Stokes problem (GS)2260
- 23. On artificial compressibility methods and further comments268
- Chapter V. Finite Element Approximation of the Navier–Stokes Equations293
- Introduction: Synopsis293
- 24. Solution of the Stokes problem with periodic boundary conditions295
- 25. A Fourier analysis of the numerical instability mechanism297
- 26. Finite element methods for the Stokes problem302
- 27. Finite element implementation of the θ -scheme (11.5)–(11.8)384
- 28. On the numerical solution of the discrete subproblems412
- 29. Further comments and complements419
- Chapter VI. Treatment of the Advection by a Wave-Like Equation Method and by Backward Methods of Cha433
- Introduction: Synopsis433
- 30. More on operator-splitting methods434
- 31. A wave-like equation method for solving the Navier–Stokes equations498
- 32. Solution of the Navier–Stokes equations by backward methods of characteristics541
- 33. On the treatment of the advection by upwinding. Final comments555
- Chapter VII. On L2-Projection Methods for the Numerical Treatment of the Incompressibility565
- Introduction: Synopsis565
- 34. Combining L2-projection methods with operator-splitting schemes à la Peaceman–Rachford and Do566
- 35. Combining L2-projection methods with operator-splitting schemes à la Marchuk–Yanenko587
- 36. Numerical experiments598
- 37. Further comments and references612
- Chapter VIII. Fictitious Domain Methods for Incompressible Viscous Flow: Application to Particulate619
- Introduction: Synopsis619
- 38. Generalities on fictitious domain methods620
- 39. On the solution of Dirichlet problems by fictitious domain methods with boundary supported Lagra622
- 40. A boundary supported Lagrange multiplier/fictitious domain method for the incompressible Navier?678
- 41. On a fictitious domain method with volume distributed Lagrange multipliers for Dirichlet problem691
- 42. On the direct numerical simulation of incompressible viscous flow with moving rigid boundary by701
- Chapter IX. Numerical Experiments771
- Introduction: Synopsis771
- 43. Flow in a nozzle at high incidence772
- 44. Application of the wave-like equation method to the numerical simulation of incompressible visco786
- 45. Numerical simulation of incompressible viscous flow a two-dimensional channel with a backward fa815
- 46. Numerical simulation of a thermal convection flow in a differentially-heated rectangular cavity836
- 47. More on particulate flow854
- 48. On blood flow in the heart873
- Chapter X. Complements: From Stream Function-Vorticity to Flow Control877
- Introduction: Synopsis877
- 49. Numerical methods for the stream function-vorticity formulation of the Navier–Stokes equations878
- 50. Simulation of Bingham visco-plastic flow940
- 51. On the numerical simulation of slightly compressible isentropic viscous flow960
- 52. Modeling and simulation of low-Mach-number compressible flows971
- 53. Optimal control of systems modeled by the incompressibleNavier–Stokes equations: Drag reductio989
- Acknowledgements1049
- References1053
- Author Index1075
- Subject Index1083
HANDBOOK OF NUMERICAL ANALYSIS IX