Handbook of numerical analysis: 9 Numerical methods for fluids ; part 3
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| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
North-Holland
2003
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| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 1176 S. Ill., graph. Darst. |
| ISBN: | 0444512241 |
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MARC
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| 245 | 1 | 0 | |a Handbook of numerical analysis |n 9 |p Numerical methods for fluids ; part 3 |c general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam |b North-Holland |c 2003 | |
| 300 | |a X, 1176 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Análisis numérico | |
| 650 | 4 | |a Flujo viscoso | |
| 700 | 1 | |a Ciarlet, Philippe G. |d 1938- |e Sonstige |0 (DE-588)143368362 |4 oth | |
| 700 | 1 | |a Lions, Jacques-Louis |d 1928-2001 |e Sonstige |0 (DE-588)124055397 |4 oth | |
| 700 | 1 | |a Du, Qiang |d 1964- |0 (DE-588)1188249320 |4 edt | |
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Record in the Search Index
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| adam_text | Contents
Preface 9
CHAPTER I. The Navier Stokes Equations for Incompressible Viscous Fluids 13
Introduction: Synopsis 13
1. Derivation of the Navier Stokes equations for viscous fluids 13
2. Initial and boundary conditions 21
3. A stream function vorticity formulation of the Navier Stokes equations 23
4. A brief introduction to Sobolev spaces 27
5. Variational formulations of the Navier Stokes equations 34
6. A short review of mathematical results for the Navier Stokes equations 48
Chapter II. A Family of Operator Splitting Methods for Initial Value Prob¬
lems. Application to the Navier Stokes Equations 51
Introduction: Synopsis 51
7. A family of initial value problems 52
8. The Peaceman Rachford method 52
9. The Douglas Rachford method 60
10. A6 scheme 63
11. Application to the Navier—Stokes equations 71
12. Further comments 73
Chapter III. Iterative Solution of the Advection Diffusion Subproblems 77
Introduction: Synopsis 77
13. Classical and variational formulations of the advection diffusion subprob¬
lems associated with the operator splitting schemes 78
14. Linear variational problems in Hilbert spaces 80
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 spaces 123
17. Least squares solution of linear and nonlinear problems in Hilbert spaces 143
18. Least squares/conjugate gradient solution of problems (13.1)and(13.2) 181
5
6 R. Glowinski
Chapter IV. Iterative Solution of the Stokes Subproblems 189
Introduction: Synopsis 189
19. Mathematical properties of the generalized Stokes problem (GS) 190
20. Gradient methods for the Stokes problem 218
21. Conjugate gradient methods for the Stokes problem (GS) i 247
22. Iterative solution of the generalized Stokes problem (GS)2 260
23. On artificial compressibility methods and further comments 268
Chapter V. Finite Element Approximation of the Navier Stokes Equations 293
Introduction: Synopsis 293
24. Solution of the Stokes problem with periodic boundary conditions 295
25. A Fourier analysis of the numerical instability mechanism 297
26. Finite element methods for the Stokes problem 302
27. Finite element implementation of the 0 scheme (11.5)—(11.8) 384
28. On the numerical solution of the discrete subproblems 412
29. Further comments and complements 419
CHAPTER VI. Treatment of the Advection by a Wave Like Equation Method
and by Backward Methods of Characteristics 433
Introduction: Synopsis 433
30. More on operator splitting methods 434
31. A wave like equation method for solving the Navier Stokes equations 498
32. Solution of the Navier Stokes equations by backward methods of charac¬
teristics 541
33. On the treatment of the advection by upwinding. Final comments 555
Chapter VII. On L2 Projection Methods for the Numerical Treatment of the
Incompressibility 565
Introduction: Synopsis 565
34. Combining L2 projection methods with operator splitting schemes a la
Peaceman Rachford and Douglas Rachford, and with the 0 scheme 566
35. Combining L2 projection methods with operator splitting schemes a la
Marchuk Yanenko 587
36. Numerical experiments 598
37. Further comments and references 612
CHAPTER VIII. Fictitious Domain Methods for Incompressible Viscous Flow:
Application to Particulate Flow 619
Introduction: Synopsis 619
38. Generalities on fictitious domain methods 620
Contents 7
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 622
40. A boundary supported Lagrange multiplier/fictitious domain method for
the incompressible Navier Stokes equations 678
41. On a fictitious domain method with volume distributed Lagrange multi¬
pliers for Dirichlet problems 691
42. On the direct numerical simulation of incompressible viscous flow with
moving rigid boundary by distributed Lagrange multiplier based fictitious
domain methods. Application to paniculate flow 701
Chapter IX. Numerical Experiments 771
Introduction: Synopsis 771
43. Flow in a nozzle at high incidence 772
44. Application of the wave like equation method to the numerical simulation
of incompressible viscous fluid flow in square and cubic cavities 786
45. Numerical simulation of incompressible viscous flow in a two dimensional
channel with a backward facing step 815
46. Numerical simulation of a thermal convection flow in a differentially
heated rectangular cavity 836
47. More on particulate flow 854
48. On blood flow in the heart 873
Chapter X. Complements: From Stream Function Vorticity to Flow Control 877
Introduction: Synopsis 877
49. Numerical methods for the stream function vorticity formulation of the
Navier Stokes equations 878
50. Simulation of Bingham visco plastic flow 940
51. On the numerical simulation of slightly compressible isentropic viscous
flow 960
52. Modeling and simulation of low Mach number compressible flows 971
53. Optimal control of systems modeled by the incompressible Navier Stokes
equations: Drag reduction by active control for flow past cylinders 989
Acknowledgements 1049
References 1053
Author Index 1075
Subject Index 1083
|
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| indexdate | 2024-07-09T18:57:57Z |
| institution | BVB |
| isbn | 0444512241 |
| language | English |
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| physical | X, 1176 S. Ill., graph. Darst. |
| publishDate | 2003 |
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| spelling | Handbook of numerical analysis 9 Numerical methods for fluids ; part 3 general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions 1. ed. Amsterdam North-Holland 2003 X, 1176 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Análisis numérico Flujo viscoso Ciarlet, Philippe G. 1938- Sonstige (DE-588)143368362 oth Lions, Jacques-Louis 1928-2001 Sonstige (DE-588)124055397 oth Du, Qiang 1964- (DE-588)1188249320 edt (DE-604)BV002745459 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009672796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Handbook of numerical analysis Análisis numérico Flujo viscoso |
| title | Handbook of numerical analysis |
| title_auth | Handbook of numerical analysis |
| title_exact_search | Handbook of numerical analysis |
| title_full | Handbook of numerical analysis 9 Numerical methods for fluids ; part 3 general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_fullStr | Handbook of numerical analysis 9 Numerical methods for fluids ; part 3 general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_full_unstemmed | Handbook of numerical analysis 9 Numerical methods for fluids ; part 3 general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_short | Handbook of numerical analysis |
| title_sort | handbook of numerical analysis numerical methods for fluids part 3 |
| topic | Análisis numérico Flujo viscoso |
| topic_facet | Análisis numérico Flujo viscoso |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009672796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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