Mathematical aspects of numerical solution of hyperbolic systems:
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
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Boca Raton [u.a.]
Chapman & Hall/CRC
2001
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| Schriftenreihe: | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics
118 |
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 540 S. graph. Darst. |
| ISBN: | 0849306086 |
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Datensatz im Suchindex
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| adam_text | K CHAPMAN & HALL/CRC MONOGRAPHS AND SURVEYS IN PURE AND APPLIED
MATHEMATICS I 18 MATHEMATICAL ASPECTS OF NUMERICAL SOLUTION OF
HYPERBOLIC SYSTEMS ANDREI G. KULIKOVSKII NIKOLAI V. POGORELOV ANDREI YU.
SEMENOV CHAPMAN & HALL/CRC BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
CONTENTS 1 HYPERBOLIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS 1 1.1
QUASILINEAR SYSTEMS 1 1.2 HYPERBOLIC SYSTEMS OF QUASILINEAR DIFFERENTIAL
EQUATIONS 2 1.2.1 DEFINITIONS 2 1.2.2 SYSTEMS OF CONSERVATION LAWS 4 1.3
MECHANICAL EXAMPLES 5 1.3.1 NONSTATIONARY EQUATIONS OF GAS DYNAMICS 5
1.3.2 STATIONARY EULER EQUATIONS 8 1.3.3 SHALLOW WATER EQUATIONS 11
1.3.4 EQUATIONS OF IDEAL MAGNETOHYDRODYNAMICS 12 1.3.5 ELASTICITY
EQUATIONS 15 1.4 PROPERTIES OF SOLUTIONS 17 1.4.1 CLASSICAL SOLUTIONS 17
1.4.2 GENERALIZED SOLUTIONS 21 1.4.3 SMALL-AMPLITUDE SHOCKS 25 1.4.4
EVOLUTIONARY CONDITIONS FOR SHOCKS 27 1.4.5 ENTROPY BEHAVIOR ON
DISCONTINUITIES 29 1.5 DISINTEGRATION OF A SMALL ARBITRARY DISCONTINUITY
31 2 NUMERICAL SOLUTION OF QUASILINEAR HYPERBOLIC SYSTEMS 33 2.1
INTRODUCTION 33 2.2 METHODS BASED ON THE EXACT SOLUTION OF THE RIEMANN
PROBLEM 37 2.2.1 THE GODUNOV METHOD OF THE FIRST ORDER. 38 2.2.2 EXACT
SOLUTION OF THE RIEMANN PROBLEM 40 2.3 METHODS BASED ON APPROXIMATE
RIEMANN PROBLEM SOLVERS 43 2.3.1 COURANT-ISAACSON-REES-TYPE METHODS 43
2.3.2 ROE S SCHEME 55 2.3.3 THE OSHER NUMERICAL SCHEME 58 2.4
GENERALIZED RIEMANN PROBLEM 65 2.5 THE GODUNOV METHOD OF THE SECOND
ORDER 67 2.6 MULTIDIMENSIONAL SCHEIHES AND THEIR STABILITY CONDITIONS 72
2.7 RECONSTRUCTION PROCEDURES AND SLOPE LIMITERS 76 2.7.1 PRELIMINARY
REMARKS 76 2.7.2 TVD SCHEMES 78 2.7.3 MONOTONE AND LIMITING
RECONSTRUCTIONS 80 2.7.4 GENUINE TVD AND TVD LIMITING RECONSTRUCTIONS 87
2.7.5 TVD LIMITERS OF NONSYMMETRIC STENCIL 92 2.7.6 MULTIDIMENSIONAL
RECONSTRUCTION 94 2.8 BOUNDARY CONDITIONS FOR HYPERBOLIC SYSTEMS 101
2.8.1 GENERAL NOTIONS 101 2.8.2 NONREFLECTING BOUNDARY CONDITIONS 102
2.8.3 EVOLUTIONARY BOUNDARY CONDITIONS 107 2.9 SHOCK-FITTING METHODS 109
2.9.1 FLOATING SHOCK FITTING 109 2.9.2 SHOCK FITTING ON MOVING GRIDS 113
2.10 ENTROPY CORRECTION PROCEDURES 115 2.11 FINAL REMARKS 119 GAS
DYNAMIC EQUATIONS 121 3.1 SYSTEMS OF GOVERNING EQUATIONS 121 3.1.1
TWO-TEMPERATURE GAS DYNAMIC EQUATIONS 124 3.1.2 THE MIXTURE OF IDEAL
GASES IN CHEMICAL NONEQUILIBRIUM 127 3.2 THE GODUNOV METHOD FOR GAS
DYNAMIC EQUATIONS 129 3.3 EXACT SOLUTION OF THE RIEMANN PROBLEM 132
3.3.1 ELEMENTARY SOLUTION 1: SHOCKWAVE 132 3.3.2 ELEMENTARY SOLUTION 2:
CONTACT DISCONTINUITY 136 3.3.3 ELEMENTARY SOLUTION 3: RAREFACTION WAVE
136 3.3.4 GENERAL EXACT SOLUTION 139 3.3.5 AN ARBITRARY EOS 147 3.4
APPROXIMATE RIEMANN PROBLEM SOLVERS 151 3.4.1 THE COURANT-ISAACSON-REES
METHOD FOR AN ARBITRARY EOS 152 3.4.2 COMPUTATION OF SHOCK-INDUCED
PHENOMENA BY THE CIR METHOD. . . 154 3.4.3 THE CIR-SIMULATION OF
JET-LIKE STRUCTURES IN LASER PLASMA 158 3.4.4 ROE S METHOD 163 3.4.5
ROE S RIEMANN PROBLEM SOLVER FOR AN ARBITRARY EOS 169 3.4.6
OSHER-SOLOMON NUMERICAL SCHEME 171 3.5 SHOCK-FITTING METHODS 175 3.5.1
DISCONTINUITIES AS BOUNDARIES OF THE COMPUTATIONAL REGION 175 3.5.2
FLOATING SHOCK-FITTING PROCEDURES 186 3.5.3 SHOCK-FITTING ON MOVING
GRIDS 189 3.5.4 SELF-ADJUSTING GRIDS 190 3.6 STATIONARY GAS DYNAMICS 197
3.6.1 SYSTEMS OF GOVERNING EQUATIONS 197 3.6.2 THE GODUNOV METHOD. THE
CIR AND ROE S SCHEMES 201 3.6.3 EXACT SOLUTION OF THE RIEMANN PROBLEM
203 3.6.4 GENERAL EXACT SOLUTION 212 3.7 SOLAR WIND - INTERSTELLAR
MEDIUM INTERACTION 213 3.7.1 PHYSICAL FORMULATION OF THE PROBLEM 213
3.7.2 NONREFLECTING BOUNDARY CONDITIONS . 218 3.7.3 NUMERICAL RESULTS
221 3.7.4 A NOTE ON GODUNOV-TYPE METHODS FOR RELATIVISTIC HYDRODYNAMICS.
. 224 SHALLOW WATER EQUATIONS 225 4.1 SYSTEM OF GOVERNING EQUATIONS 225
4.2 THE GODUNOV METHOD FOR SHALLOW WATER EQUATIONS 228 4.3 EXACT
SOLUTION OF THE RIEMANN PROBLEM V . . 231 4.3.1 ELEMENTARY SOLUTION 1:
HYDRAULIC JUMP 231 4.3.2 ELEMENTARY SOLUTION 2: TANGENTIAL
DISCONTINUITY. 235 4.3.3 ELEMENTARY SOLUTION 3: RIEMANN WAVE 235 4.3.4
GENERAL EXACT SOLUTION 237 4.4 RESULTS OF NUMERICAL ANALYSIS 245 4.5
APPROXIMATE RIEMANN PROBLEM SOLVERS 257 4.5.1 THE CIR METHOD 257 4.5.2
ROE S METHOD 258 4.5.3 THE OSHER-SOLOMON SOLVER. 261 4.6 STATIONARY
SHALLOW WATER EQUATIONS 262 4.6.1 SYSTEM OF GOVERNING EQUATIONS 263
4.6.2 THE GODUNOV METHOD. THE CIR AND ROE S SCHEMES 265 4.6.3 EXACT
SOLUTION OF THE RIEMANN PROBLEM 266 4.6.4 GENERAL EXACT SOLUTION 275
MAGNETOHYDRODYNAMIC EQUATIONS 277 5.1 MHD SYSTEM IN THE CONSERVATION-LAW
FORM 277 5.2 CLASSIFICATION OF MHD DISCONTINUITIES 285 5.3 EVOLUTIONARY
MHD SHOCKS 288 5.3.1 EVOLUTIONARY DIAGRAM 288 5.3.2 CONVENIENT RELATIONS
ON MHD SHOCKS 290 5.3.3 EVOLUTIONARITY OF PERPENDICULAR, PARALLEL, AND
SINGULAR SHOCKS. . . 291 5.3.4 JOUGET POINTS 294 5.4 HIGH-RESOLUTION
NUMERICAL SCHEMES FOR MHD EQUATIONS 295 5.4.1 THE OSHER-TYPE METHOD .
296 5.4.2 PIECEWISE-PARABOLIC METHOD 297 5.4.3 ROE S CHARACTERISTIC
DECOMPOSITION METHOD 298 5.4.4 NUMERICAL TESTS WITH THE ROE-TYPE SCHEME.
305 5.4.5 MODIFIED MHD SYSTEM 323 5.5 SHOCK-CAPTURING APPROACH AND
NONEVOLUTIONARY SOLUTIONS IN MHD .... 328 5.5.1 PRELIMINARY REMARKS 328
5.5.2 SIMPLIFIED MHD EQUATIONS AND RELATED DISCONTINUITIES 332 5.5.3
SHOCK STRUCTURE IN SOLUTIONS OF THE SIMPLIFIED SYSTEM 333 5.5.4
NONSTATIONARY PROCESSES IN THE STRUCTURE OF NONEVOLUTIONARY SHOCK WAVES
* * * * 335 5.5.5 NUMERICAL EXPERIMENTS BASED ON THE FULL SET OF MHD
EQUATIONS. . 337 5.5.6 NUMERICAL DISINTEGRATION OF A COMPOUND WAVE 339
5.6 STRONG BACKGROUND MAGNETIC FIELD 345 5.7 ELIMINATION OF NUMERICAL
MAGNETIC CHARGE 348 XLL 5.7.1 PRELIMINARY REMARKS 348 5.7.2 APPLICATION
OF THE VECTOR POTENTIAL 349 5.7.3 THE USE OF AN ARTIFICIAL SCALAR
POTENTIAL 350 5.7.4 _ APPLICATION OF THE MODIFIED MHD SYSTEM 351 5.7.5
APPLICATION OF STAGGERED GRIDS 352 5.8 SOLAR WIND INTERACTION WITH THE
MAGNETIZED INTERSTELLAR MEDIUM 356 5.8.1 STATEMENT OF THE PROBLEM 357
5.8.2 NUMERICAL ALGORITHM 359 5.8.3 NUMERICAL RESULTS: AXISYMMETRIC CASE
363 5.8.4 NUMERICAL RESULTS: ROTATIONALLY PERTURBED FLOW 368 5.8.5 A
NOTE ON THE MHD FLOW OVER AN INFINITELY CONDUCTING CYLINDER. . 372 5.8.6
NUMERICAL RESULTS: THREE-DIMENSIONAL MODELLING 374 6 SOLID DYNAMICS
EQUATIONS 379 6.1 SYSTEM OF GOVERNING EQUATIONS 379 6.1.1 SOLID DYNAMICS
WITH AN ARBITRARY EOS 380 6.1.2 CONSERVATIVE FORM OF ELASTOVISCOPLASTIC
SOLID DYNAMICS 392 6.1.3 DYNAMICS OF THIN SHELLS 396 6.2 CIR METHOD FOR
THE CALCULATION OF SOLID DYNAMICS PROBLEMS 399 6.2.1 NUMERICAL
SIMULATION OF SPALLATION PHENOMENA 404 6.3 CIR METHOD FOR STUDYING THE
DYNAMICS OF THIN SHELLS 410 6.3.1 THE KLEIN-GORDON EQUATION 415 6.3.2
DYNAMICS EQUATIONS OF CYLINDRICAL SHELLS. . . . X . 416 6.3.3 DYNAMICS
EQUATIONS OF ORTHOTROPIC SHELLS 418 6.3.4 SELECTION OF RAPIDLY
OSCILLATING COMPONENTS 419 7 NONCLASSICAL DISCONTINUITIES AND SOLUTIONS
OF HYPERBOLIC SYSTEMS 423 7.1 EVOLUTIONARY CONDITIONS IN NONCLASSICAL
CASES 425 7.2 STRUCTURE OF FRONTS. ADDITIONAL BOUNDARY CONDITIONS ON THE
FRONTS 427 7.2.1 EQUATIONS DESCRIBING THE DISCONTINUITY STRUCTURE 429
7.2.2 FORMULATION OF THE STRUCTURE PROBLEM AND ADDITIONAL ASSUMPTIONS.
431 -7:2.3 BEHAVIOR OF THE SOLUTION AS -+ OO 432 7.2.4 ADDITIONAL
RELATIONS ON DISCONTINUITIES 434 7.2.5 MAIN RESULT AND ITS DISCUSSION
435 7.2.6 A REMARK ON DERIVING ADDITIONAL RELATIONS WHEN CONDITION
(7.2.7) IS NOT SATISFIED 436 7.2.7 HUGONIOT MANIFOLD 438 7.3 BEHAVIOR
OF THE HUGONIOT CURVE IN THE VICINITY OF JOUGET POINTS AND NONUNIQUENESS
OF SOLUTIONS OF SELF-SIMILAR PROBLEMS 439 7.4 NONLINEAR SMALL-AMPLITUDE
WAVES IN ANISOTROPIC ELASTIC MEDIA 447 7.4.1 BASIC EQUATIONS 447 7.4.2
QUASILONGITUDINAL WAVES 449 7.4.3 QUASITRANSVERSE WAVES 450 7.4.4
RIEMANN WAVES 451 7.4.5 SHOCKWAVES 452 XM 7.4.6 SELF-SIMILAR PROBLEMS
AND NONUNIQUENESS OF SOLUTIONS. 455 7.4.7 WAVES IN VISCOELASTIC MEDIA,
VANISHING VISCOSITY 456 7.4.8 ROLE OF THE WAVE ANISOTROPY AND PASSAGE TO
THE LIMIT G - 0. ... 459 7.4.9 FINAL CONCLUSIONS 460 7.5
ELECTROMAGNETIC SHOCK WAVES IN FERROMAGNETS 461 7.5.1 LONG-WAVE
APPROXIMATION. ELASTIC ANALOGY. 461 7.5.2 STRUCTURE OF ELECTROMAGNETIC
SHOCK WAVES 464 7.5.3 THE SET OF ADMISSIBLE DISCONTINUITIES 470 7.5.4
NONUNIQUENESS OF SOLUTIONS 470 7.6 SHOCK WAVES IN COMPOSITE MATERIALS
472 7.6.1 BASIC EQUATIONS AND THE DISCONTINUITY STRUCTURE 472 7.6.2
DISCONTINUITY STRUCTURE; ADMISSIBLE DISCONTINUITIES 474 7.6.3 CASEFC 0
474 7.6.4 CASEFC 0 478 7.7 LONGITUDINAL NONLINEAR WAVES IN ELASTIC RODS
479 7.7.1 LARGE-SCALE MODEL 479 7.7.2 MODEL FOR MODERATE-SCALE MOTIONS
481 7.7.3 EQUATIONS DESCRIBING THE DISCONTINUITY STRUCTURE 482 7.7.4
ADMISSIBLE DISCONTINUITIES 483 7.7.5 MORE PRECISE LARGE-SCALE MODEL.
NONUNIQUENESS 486 7.8 IONIZATION FRONTS IN A MAGNETIC FIELD 487 7.8.1
LARGE-SCALE MODEL 487 7.8.2 MODERATE-SCALE MODEL 488 7.8.3 THE SET OF
ADMISSIBLE DISCONTINUITIES 490 7.8.4 THE SIMPLEST SELF-SIMILAR PROBLEM
494 7.8.5 VARIATION OF THE GAS VELOCITY ACROSS IONIZATION FRONTS 495
7.8.6 CONSTRUCTING THE SOLUTION OF THE PISTON PROBLEM 500 7.9 DISCUSSION
501 BIBLIOGRAPHY 503 INDEX 535
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| spelling | Kulikovskij, Andrej G. Verfasser aut Mathematical aspects of numerical solution of hyperbolic systems Andrei G. Kulikovskii ; Nikolai V. Pogorelov ; Andrei Yu. Semenov Boca Raton [u.a.] Chapman & Hall/CRC 2001 XIII, 540 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 118 Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Pogorelov, Nikolaj V. Verfasser aut Semenov, Andrej Ju. Verfasser aut Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 118 (DE-604)BV013350872 118 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009325255&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kulikovskij, Andrej G. Pogorelov, Nikolaj V. Semenov, Andrej Ju Mathematical aspects of numerical solution of hyperbolic systems Chapman & Hall/CRC monographs and surveys in pure and applied mathematics Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4131213-2 (DE-588)4128130-5 |
| title | Mathematical aspects of numerical solution of hyperbolic systems |
| title_auth | Mathematical aspects of numerical solution of hyperbolic systems |
| title_exact_search | Mathematical aspects of numerical solution of hyperbolic systems |
| title_full | Mathematical aspects of numerical solution of hyperbolic systems Andrei G. Kulikovskii ; Nikolai V. Pogorelov ; Andrei Yu. Semenov |
| title_fullStr | Mathematical aspects of numerical solution of hyperbolic systems Andrei G. Kulikovskii ; Nikolai V. Pogorelov ; Andrei Yu. Semenov |
| title_full_unstemmed | Mathematical aspects of numerical solution of hyperbolic systems Andrei G. Kulikovskii ; Nikolai V. Pogorelov ; Andrei Yu. Semenov |
| title_short | Mathematical aspects of numerical solution of hyperbolic systems |
| title_sort | mathematical aspects of numerical solution of hyperbolic systems |
| topic | Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Hyperbolische Differentialgleichung Numerisches Verfahren |
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