Numerical solution of convection diffusion problems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1996
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Applied mathematics and mathematical computation
12 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007061884&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 372 S. Ill., graph. Darst. |
| ISBN: | 0412564408 |
Internformat
MARC
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| 100 | 1 | |a Morton, Keith W. |d 1930- |e Verfasser |0 (DE-588)172264766 |4 aut | |
| 245 | 1 | 0 | |a Numerical solution of convection diffusion problems |c K. W. Morton |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1996 | |
| 300 | |a XII, 372 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematics and mathematical computation |v 12 | |
| 650 | 7 | |a Calculs numériques |2 ram | |
| 650 | 7 | |a Equations de réaction-diffusion |2 ram | |
| 650 | 7 | |a Fluides, dynamique des - Mathématiques |2 ram | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Fluid dynamics |x Mathematics | |
| 650 | 4 | |a Numerical calculations | |
| 650 | 4 | |a Reaction-diffusion equations | |
| 650 | 0 | 7 | |a Diffusion |0 (DE-588)4012277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007061884 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 671f 2001 A 25572 0701 0015 A 979 |
|---|---|
| DE-BY-TUM_katkey | 774762 |
| DE-BY-TUM_location | 01 Mag |
| DE-BY-TUM_media_number | 040020231543 040020817596 |
| _version_ | 1821931419049394176 |
| adam_text | Contents
Preface ix
1 Introduction and overview 1
1.1 Typical problems where convection diffusion occurs 1
1.2 Model problems 9
1.3 Numerical difficulties with simple difference schemes 12
1.3.1 Central difference scheme 13
1.3.2 Upwind difference scheme 18
1.3.3 Truncation error and global error 21
1.3.4 Graded meshes 23
1.4 Finite elements in one dimension 24
1.4.1 Discrete equations for piecewise linear approximation 24
1.4.2 Outline error analysis 28
1.4.3 Unsteady problems 29
1.4.4 A posteriori error analysis 31
1.5 Iterative solution of discrete equations 35
1.6 Overview of effective methods 39
2 Selected results from mathematical analysis 43
2.1 Introduction 43
2.2 Maximum principles 45
2.3 Boundary and interior layers in one dimension 47
2.3.1 Problems with no turning points 49
2.3.2 Turning point problems 50
2.4 Derivative bounds in a one dimensional boundary layer 53
2.5 Weak formulation of the problem 58
2.6 A priori bounds and boundary layers in two dimensions 60
2.7 Green s functions 65
2.7.1 One dimensional examples 67
2.7.2 Free space Green s functions 71
3 Difference schemes for steady problems 75
vi CONTENTS
3.1 One dimensional problems 75
3.2 Hermitian and Operator Compact Implicit (OCI) schemes 77
3.2.1 Derivation of the standard scheme 78
3.2.2 Properties of OCI and related schemes 79
3.2.3 Generalised OCI schemes 81
3.3 Exponential fitting and locally exact schemes 84
3.3.1 Exponentially fitted schemes 84
3.3.2 Locally exact schemes 87
3.4 Error analysis by a maximum principle 91
3.4.1 The simple upwind scheme 92
3.4.2 The Allen and Southwell scheme 95
3.4.3 Exponential fitting and uniform error bounds 98
3.5 Turning point problems 101
3.6 Simple extensions to two dimensions 102
3.6.1 Maximum principles 103
3.6.2 Typical difference schemes and error bounds 105
3.6.3 Crosswind diffusion 109
3.6.4 Adaptive and nonlinear difference schemes 111
4 Finite element methods: Galerkin schemes 113
4.1 Triangular and quadrilateral meshes 114
4.1.1 Local mapping for a triangle 115
4.1.2 Local mapping for a quadrilateral 116
4.2 Standard error bounds for Galerkin schemes 118
4.2.1 Approximation properties of the trial spaces 118
4.2.2 A general error bound 120
4.2.3 Inverse estimates for the trial spaces 121
4.3 Galerkin methods on a triangular mesh 121
4.3.1 Linear approximation 121
4.3.2 Quadratic approximation 126
4.4 Galerkin methods on quadrilaterals 132
4.4.1 Isoparametric bilinear approximation 132
4.4.2 Biquadratic approximation 137
4.5 Comparative approximation properties 141
4.6 Numerical comparisons of accuracy 144
4.6.1 One dimension, constant b 144
4.6.2 A one dimensional conservation law 147
4.6.3 The first IAHR/CEGB problem 150
5 Petrov Galerkin methods 153
5.1 Up winded test functions 154
5.2 Approximate symmetrization 155
5.2.1 Symmetrization based on B { , •) 159
5.2.2 Symmetrization based on i?2( ) 160
CONTENTS vii
5.3 Hemker test functions 163
5.4 Error bounds in Lx and L2 norms 165
5.5 Streamline diffusion methods 166
5.6 Comparative error estimates 169
5.6.1 One dimensional model problem 169
5.6.2 Two dimensional problems 175
5.7 Error analysis of the streamline diffusion method 179
5.7.1 One dimensional model problem 179
5.7.2 Two dimensional problems 182
5.8 Use of local Green s functions 192
5.8.1 One dimensional analysis 193
5.8.2 Extensions to two dimensions 202
5.9 A mixed norm method 204
5.9.1 In one dimension 205
5.9.2 In two dimensions 208
5.10 Numerical comparisons 210
5.10.1 The one dimensional conservation law 210
5.10.2 The IAHR/CEGB problems 210
6 Finite volume methods for steady problems 215
6.1 Introduction 215
6.2 Difference based methods 218
6.2.1 Convective fluxes 219
6.2.2 Time stepping to steady state 220
6.2.3 Solution adaptive schemes 226
6.2.4 A central/upwind difference example 232
6.3 Finite element based methods 234
6.3.1 Cell centre schemes 235
6.3.2 Spurious modes and artificial dissipation 237
6.3.3 Runge Kutta time stepping 241
6.3.4 Cell vertex methods 243
6.3.5 Recovery of gradients 246
6.3.6 Distribution matrices and artificial dissipation 250
6.3.7 Vertex centred schemes 254
6.3.8 Unstructured triangular meshes 256
6.4 Cell vertex analysis in one dimension 258
6.4.1 Monotonicity properties, maximum principles and
supraconvergence 259
6.4.2 Error estimates in discrete energy norms 264
6.5 Cell vertex analysis in two dimensions 273
6.5.1 Distribution matrices and resolution of the counting
problem 274
6.5.2 Spurious modes, least squares and artificial dissipation278
6.5.3 Coercivity for the continuous problem 280
viii CONTENTS
6.5.4 Error bounds in a discrete energy norm 281
6.6 Two simple nonlinear problems 289
6.6.1 Burgers equation 290
6.6.2 One dimensional Euler equations 293
7 Unsteady problems 297
7.1 Introduction 297
7.2 Evolution Galerkin and semi Lagrangian methods 300
7.2.1 Taylor Galerkin methods 300
7.2.2 Lagrange Galerkin and characteristic Galerkin
methods 303
7.2.3 Area weighting techniques 313
7.2.4 Adaptive recovery techniques 315
7.2.5 Examples of PERU schemes 323
7.2.6 Semi Lagrangian methods 327
7.2.7 Use of a fundamental solution 332
7.2.8 Some stability and convergence results 334
7.3 Generalised Godunov schemes 342
7.3.1 Explicit schemes 343
7.3.2 Generalised box schemes 346
7.4 Semi discrete based schemes 349
References 353
Index 366
|
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| author | Morton, Keith W. 1930- |
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV010590058 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:57:12Z |
| institution | BVB |
| isbn | 0412564408 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007061884 |
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| owner_facet | DE-20 DE-29T DE-91G DE-BY-TUM DE-703 DE-858 DE-634 DE-83 DE-188 DE-11 DE-706 |
| physical | XII, 372 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Applied mathematics and mathematical computation |
| series2 | Applied mathematics and mathematical computation |
| spellingShingle | Morton, Keith W. 1930- Numerical solution of convection diffusion problems Applied mathematics and mathematical computation Calculs numériques ram Equations de réaction-diffusion ram Fluides, dynamique des - Mathématiques ram Mathematik Fluid dynamics Mathematics Numerical calculations Reaction-diffusion equations Diffusion (DE-588)4012277-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Konvektion (DE-588)4117572-4 gnd |
| subject_GND | (DE-588)4012277-3 (DE-588)4128130-5 (DE-588)4117572-4 |
| title | Numerical solution of convection diffusion problems |
| title_auth | Numerical solution of convection diffusion problems |
| title_exact_search | Numerical solution of convection diffusion problems |
| title_full | Numerical solution of convection diffusion problems K. W. Morton |
| title_fullStr | Numerical solution of convection diffusion problems K. W. Morton |
| title_full_unstemmed | Numerical solution of convection diffusion problems K. W. Morton |
| title_short | Numerical solution of convection diffusion problems |
| title_sort | numerical solution of convection diffusion problems |
| topic | Calculs numériques ram Equations de réaction-diffusion ram Fluides, dynamique des - Mathématiques ram Mathematik Fluid dynamics Mathematics Numerical calculations Reaction-diffusion equations Diffusion (DE-588)4012277-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Konvektion (DE-588)4117572-4 gnd |
| topic_facet | Calculs numériques Equations de réaction-diffusion Fluides, dynamique des - Mathématiques Mathematik Fluid dynamics Mathematics Numerical calculations Reaction-diffusion equations Diffusion Numerisches Verfahren Konvektion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007061884&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV006188231 |
| work_keys_str_mv | AT mortonkeithw numericalsolutionofconvectiondiffusionproblems |
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