Numerical methods for conservation laws:
Gespeichert in:
| Späterer Titel: | LeVeque, Randall J. Finite volume methods for hyperbolic problems |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1992
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Lectures in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | 214 S. graph. Darst. |
| ISBN: | 9783764327231 3764327235 0817627235 |
Internformat
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| 245 | 1 | 0 | |a Numerical methods for conservation laws |c Randall J. LeVeque |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1992 | |
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Datensatz im Suchindex
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| adam_text | RANDALL J. LEVEQUE NUMERICAL METHODS FOR CONSERVATION LAWS SECOND
EDITION 1992 BIRKHAEUSER VERLAG BASEL * BOSTON * BERLIN CONTENTS I
MATHEMATICAL THEORY VII 1 INTRODUCTION 1 1.1 CONSERVATION LAWS 1 1.2
APPLICATIONS 2 1.3 MATHEMATICAL DIFFICULTIES 8 1.4 NUMERICAL
DIFFICULTIES 9 1.5 SOME REFERENCES 12 2 THE DERIVATION OF CONSERVATION
LAWS 14 2.1 INTEGRAL AND DIFFERENTIAL FORMS 14 2.2 SCALAR EQUATIONS 16
2.3 DIFFUSION 17 3 SCALAR CONSERVATION LAWS 19 3.1 THE LINEAR ADVECTION
EQUATION 19 3.1.1 DOMAIN OF DEPENDENCE 20 3.1.2 NONSMOOTH DATA 21 3.2
BURGERS EQUATION 23 3.3 SHOCK FORMATION 25 3.4 WEAK SOLUTIONS 27 3.5
THE RIEMANN PROBLEM 28 3.6 SHOCK SPEED 31 3.7 MANIPULATING CONSERVATION
LAWS 34 3.8 ENTROPY CONDITIONS 36 3.8.1 ENTROPY FUNCTIONS 37 4 SOME
SCALAR EXAMPLES 41 4.1 TRAFFIC FLOW 41 4.1.1 CHARACTERISTICS AND SOUND
SPEED 44 4.2 TWO PHASE FLOW 48 CONTENTS 5 SOM E NONLINEAR SYSTEMS 51
5.1 THE EULER EQUATIONS 51 5.1.1 IDEAL GAS 53 5.1.2 ENTROPY 54 5.2
ISENTROPIC FLOW 55 5.3 ISOTHERMAL FLOW 56 5.4 THE SHALLOW WATER
EQUATIONS 56 6 LINEAR HYPERBOLIC SYSTEMS 58 6.1 CHARACTERISTIC VARIABLES
58 6.2 SIMPLE WAVES 60 6.3 THE WAVE EQUATION 60 6.4 LINEARIZATION OF
NONLINEAR SYSTEMS 61 6.4.1 SOUND WAVES 63 6.5 THE RIEMANN PROBLEM 64
6.5.1 THE PHASE PLANE 67 7 SHOCKS AND THE HUGONIOT LOCUS 70 7.1 THE
HUGONIOT LOCUS 70 7.2 SOLUTION OF THE RIEMANN PROBLEM 73 7.2.1 RIEMANN
PROBLEMS WITH NO SOLUTION 75 7.3 GENUINE NONLINEARITY 75 7.4 THE LAX
ENTROPY CONDITION 76 7.5 LINEAR DEGENERACY 78 7.6 THE RIEMANN PROBLEM 79
8 RAREFACTION WAVES AND INTEGRAL CURVES 81 8.1 INTEGRAL CURVES 81 8.2
RAREFACTION WAVES 82 8.3 GENERAL SOLUTION OF THE RIEMANN PROBLEM 86 8.4
SHOCK COLLISIONS 88 9 THE RIEMANN PROBLEM FOR THE EULER EQUATIONS 89 9.1
CONTACT DISCONTINUITIES 89 9.2 SOLUTION TO THE RIEMANN PROBLEM 91
CONTENTS II NUMERICAL METHODS 95 10 NUMERICAL METHODS FOR LINEAR
EQUATIONS 97 10.1 THE GLOBAL ERROR AND CONVERGENCE 102 10.2 NORMS 103
10.3 LOCAL TRUNCATION ERROR 104 10.4 STABILITY 106 10.5 THE LAX
EQUIVALENCE THEOREM 107 10.6 THE CFL CONDITION 110 10.7 UPWIND METHODS
112 11 COMPUTING DISCONTINUOUS SOLUTIONS 114 11.1 MODIFIED EQUATIONS 117
11.1.1 FIRST ORDER METHODS AND DIFFUSION 118 11.1.2 SECOND ORDER METHODS
AND DISPERSION 119 11.2 ACCURACY 121 12 CONSERVATIVE METHODS FOR
NONLINEAR PROBLEMS 122 12.1 CONSERVATIVE METHODS 124 12.2 CONSISTENCY
126 12.3 DISCRETE CONSERVATION 128 12.4 THE LAX-WENDROFF THEOREM 129
12.5 THE ENTROPY CONDITION 133 13 GODUNOV S METHOD 136 13.1 THE
COURANT-ISAACSON-REES METHOD 137 13.2 GODUNOV S METHOD 138 13.3 LINEAR
SYSTEMS 140 13.4 THE ENTROPY CONDITION 142 13.5 SCALAR CONSERVATION LAWS
143 14 APPROXIMATE RIEMANN SOLVERS 146 14.1 GENERAL THEORY 147 14.1.1
THE ENTROPY CONDITION 148 14.1.2 MODIFIED CONSERVATION LAWS 149 14.2
ROE S APPROXIMATE RIEMANN SOLVER 149 14.2.1 THE NUMERICAL FLUX FUNCTION
FOR ROE S SOLVER 150 14.2.2 A SONIC ENTROPY FIX 151 14.2.3 THE SCALAR
CASE 153 14.2.4 A ROE MATRIX FOR ISOTHERMAL FLOW 156 CONTENTS 15
NONLINEAR STABILITY 158 15.1 CONVERGENCE NOTIONS 158 15.2 COMPACTNESS
159 15.3 TOTAL VARIATION STABILITY 162 15.4 TOTAL VARIATION DIMINISHING
METHODS 165 15.5 MONOTONICITY PRESERVING METHODS 165 15.6 /J-CONTRACTING
NUMERICAL METHODS 166 15.7 MONOTONE METHODS 169 16 HIGH RESOLUTION
METHODS 173 16.1 ARTIFICIAL VISCOSITY 173 16.2 FLUX-LIMITER METHODS 176
16.2.1 LINEAR SYSTEMS 182 16.3 SLOPE-LIMITER METHODS 183 16.3.1 LINEAR
SYSTEMS 187 16.3.2 NONLINEAR SCALAR EQUATIONS 188 16.3.3 NONLINEAR
SYSTEMS 191 17 SEMI-DISCRETE METHODS 193 17.1 EVOLUTION EQUATIONS FOR
THE CELL AVERAGES 193 17.2 SPATIAL ACCURACY 195 17.3 RECONSTRUCTION BY
PRIMITIVE FUNCTIONS 196 17.4 ENO SCHEMES 198 18 MULTIDIMENSIONAL
PROBLEMS 200 18.1 SEMI-DISCRETE METHODS 201 18.2 SPLITTING METHODS 202
18.3 TVD METHODS 206 18.4 MULTIDIMENSIONAL APPROACHES 206 BIBLIOGRAPHY
208
|
| any_adam_object | 1 |
| author | LeVeque, Randall J. 1955- |
| author_GND | (DE-588)112053688 |
| author_facet | LeVeque, Randall J. 1955- |
| author_role | aut |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Bauingenieurwesen Mathematik Vermessungswesen |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:17:20Z |
| institution | BVB |
| isbn | 9783764327231 3764327235 0817627235 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002931620 |
| oclc_num | 25281500 |
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| owner | DE-384 DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-739 DE-20 DE-29T DE-M347 DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
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| physical | 214 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
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| spelling | LeVeque, Randall J. 1955- Verfasser (DE-588)112053688 aut Numerical methods for conservation laws Randall J. LeVeque 2. ed. Basel [u.a.] Birkhäuser 1992 214 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics Hier auch später erschienene, unveränderte Nachdrucke Conservation laws (Mathematics) Differential equations, Hyperbolic Numerical solutions Shock waves Nichtlineares hyperbolisches System (DE-588)4191896-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 s Nichtlineares hyperbolisches System (DE-588)4191896-4 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Hyperbolische Differentialgleichung (DE-588)4131213-2 s Numerische Mathematik (DE-588)4042805-9 s Später u.d.T.: LeVeque, Randall J. Finite volume methods for hyperbolic problems GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002931620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | LeVeque, Randall J. 1955- Numerical methods for conservation laws Conservation laws (Mathematics) Differential equations, Hyperbolic Numerical solutions Shock waves Nichtlineares hyperbolisches System (DE-588)4191896-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| subject_GND | (DE-588)4191896-4 (DE-588)4128130-5 (DE-588)4131213-2 (DE-588)4042805-9 (DE-588)4131214-4 |
| title | Numerical methods for conservation laws |
| title_auth | Numerical methods for conservation laws |
| title_exact_search | Numerical methods for conservation laws |
| title_full | Numerical methods for conservation laws Randall J. LeVeque |
| title_fullStr | Numerical methods for conservation laws Randall J. LeVeque |
| title_full_unstemmed | Numerical methods for conservation laws Randall J. LeVeque |
| title_new | LeVeque, Randall J. Finite volume methods for hyperbolic problems |
| title_short | Numerical methods for conservation laws |
| title_sort | numerical methods for conservation laws |
| topic | Conservation laws (Mathematics) Differential equations, Hyperbolic Numerical solutions Shock waves Nichtlineares hyperbolisches System (DE-588)4191896-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| topic_facet | Conservation laws (Mathematics) Differential equations, Hyperbolic Numerical solutions Shock waves Nichtlineares hyperbolisches System Numerisches Verfahren Hyperbolische Differentialgleichung Numerische Mathematik Erhaltungssatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002931620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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