Riemann solvers and numerical methods for fluid dynamics: a practical introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 599 - 624 |
| Beschreibung: | XIX, 624 S. Ill., graph. Darst. |
| ISBN: | 3540659668 |
Internformat
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| 245 | 1 | 0 | |a Riemann solvers and numerical methods for fluid dynamics |b a practical introduction |c Eleuterio F. Toro |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XIX, 624 S. |b Ill., graph. Darst. | ||
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| 500 | |a Literaturverz. S. 599 - 624 | ||
| 650 | 7 | |a Fluides, Dynamique des - Informatique |2 ram | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 4 | |a Fluid dynamics |x Data processing | |
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Datensatz im Suchindex
| _version_ | 1804127213480574976 |
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| adam_text | ELEUTERIO R TORO RIEMANN SOLVERS AND NUMERICAL METHODS FOR FLUID
DYNAMICS A PRACTICAL INTRODUCTION 2 ND EDITION WITH 247 FIGURES AND 26
TABLES SPRINGER TABLE OF CONTENTS PREFACE TO THE FIRST EDITION V 1. THE
EQUATIONS OF FLUID DYNAMICS 1 1.1 THE EULER EQUATIONS 2 1.1.1
CONSERVATION-LAW FORM 3 1.1.2 OTHER COMPACT FORMS 4 1.2 THERMODYNAMIC
CONSIDERATIONS .. 5 1.2.1 UNITS OF MEASURE 5 1.2.2 EQUATIONS OF STATE
(EOS) 6 1.2.3 OTHER VARIABLES AND RELATIONS 7 1.2.4 IDEAL GASES 11 1.2.5
COVOLUME AND VAN DER WAAL GASES 13 1.3 VISCOUS STRESSES 15 1.4 HEAT
CONDUCTION 17 1.5 INTEGRAL FORM OF THE EQUATIONS 18 1.5.1 TIME
DERIVATIVES 19 1.5.2 CONSERVATION OF MASS 20 1.5.3 CONSERVATION OF
MOMENTUM 21 1.5.4 CONSERVATION OF ENERGY 23 1.6 SUBMODELS 25 1.6.1
SUMMARY OF THE EQUATIONS 25 1.6.2 FLOW WITH AREA VARIATION 27 1.6.3
AXI-SYMMETRIC FLOWS 28 1.6.4 CYLINDRICAL AND SPHERICAL SYMMETRY 29 1.6.5
PLAIN ONE-DIMENSIONAL FLOW 29 1.6.6 STEADY COMPRESSIBLE FLOW 32 1.6.7
VISCOUS COMPRESSIBLE FLOW 33 1.6.8 FREE-SURFACE GRAVITY FLOW 33 1.6.9
THE SHALLOW WATER EQUATIONS 35 1.6.10 INCOMPRESSIBLE VISCOUS FLOW 38
1.6.11 THE ARTIFICIAL COMPRESSIBILITY EQUATIONS 39 XII TABLE OF CONTENTS
2. NOTIONS ON HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS 41 2.1
QUASI-LINEAR EQUATIONS: BASIC CONCEPTS 41 2.2 THE LINEAR ADVECTION
EQUATION 47 2.2.1 CHARACTERISTICS AND THE GENERAL SOLUTION 47 2.2.2 THE
RIEMANN PROBLEM 49 2.3 LINEAR HYPERBOLIC SYSTEMS 50 2.3.1
DIAGONALISATION AND CHARACTERISTIC VARIABLES 51 2.3.2 THE GENERAL
INITIAL-VALUE PROBLEM 52 2.3.3 THE RIEMANN PROBLEM 55 2.3.4 THE RIEMANN
PROBLEM FOR LINEARISED GAS DYNAMICS .. 58 2.3.5 SOME USEFUL DEFINITIONS
59 2.4 CONSERVATION LAWS 60 2.4.1 INTEGRAL FORMS OF CONSERVATION LAWS 61
2.4.2 NON-LINEARITIES AND SHOCK FORMATION 65 2.4.3 CHARACTERISTIC FIELDS
...* 76 2.4.4 ELEMENTARY-WAVE SOLUTIONS OF THE RIEMANN PROBLEM . 83 3.
SOME PROPERTIES OF THE EULER EQUATIONS 87 3.1 THE ONE-DIMENSIONAL EULER
EQUATIONS .... : 87 3.1.1 CONSERVATIVE FORMULATION 87 3.1.2
NON-CONSERVATIVE FORMULATIONS 91 3.1.3 ELEMENTARY WAVE SOLUTIONS OF THE
RIEMANN PROBLEM.. 94 3.2 MULTI-DIMENSIONAL EULER EQUATIONS 102 3.2.1
TWO-DIMENSIONAL EQUATIONS IN CONSERVATIVE FORM ... 103 3.2.2
THREE-DIMENSIONAL EQUATIONS IN CONSERVATIVE FORM .. 107 3.2.3
THREE-DIMENSIONAL PRIMITIVE VARIABLE FORMULATION ... 108 3.2.4 THE SPLIT
THREE-DIMENSIONAL RIEMANN PROBLEM 110 3.3 CONSERVATIVE VERSUS
NON-CONSERVATIVE FORMULATIONS ILL 4. THE RIEMANN PROBLEM FOR THE EULER
EQUATIONS 115 4.1 SOLUTION STRATEGY 116 4.2 EQUATIONS FOR PRESSURE AND
PARTICLE VELOCITY 119 4.2.1 FUNCTION / L FOR A LEFT SHOCK 120 4.2.2
FUNCTION /L FOR LEFT RAREFACTION 122 4.2.3 FUNCTION / R FOR A RIGHT
SHOCK 123 4.2.4 FUNCTION /R FOR A RIGHT RAREFACTION 124 4.3 NUMERICAL
SOLUTION FOR PRESSURE 125 4.3.1 BEHAVIOUR OF THE PRESSURE FUNCTION 125
4.3.2 ITERATIVE SCHEME FOR FINDING THE PRESSURE 127 4.3.3 NUMERICAL
TESTS 129 4.4 THE COMPLETE SOLUTION 133 4.5 SAMPLING THE SOLUTION 136
4.5.1 LEFT SIDE OF CONTACT: S = X/T T 137 4.5.2 RIGHT SIDE OF CONTACT: S
= X/T U* 137 4.6 THE RIEMANN PROBLEM IN THE PRESENCE OF VACUUM 138 TABLE
OF CONTENTS XIII 4.6.1 CASE 1: VACUUM RIGHT STATE 140 4.6.2 CASE 2:
VACUUM LEFT STATE 141 4.6.3 CASE 3: GENERATION OF VACUUM 142 4.7 THE
RIEMANN PROBLEM FOR COVOLUME GASES 143 4.7.1 SOLUTION FOR PRESSURE AND
PARTICLE VELOCITY 144 4.7.2 NUMERICAL SOLUTION FOR PRESSURE 147 4.7.3
THE COMPLETE SOLUTION 147 4.7.4 SOLUTION INSIDE RAREFACTIONS 148 4.8 THE
SPLIT MULTI-DIMENSIONAL CASE 149 4.9 FORTRAN PROGRAM FOR EXACT RIEMANN
SOLVER 151 5. NOTIONS ON NUMERICAL METHODS 163 5.1 DISCRETISATION:
INTRODUCTORY CONCEPTS 163 5.1.1 APPROXIMATION TO DERIVATIVES 164 5.1.2
FINITE DIFFERENCE APPROXIMATION TO A PDE 165 5.2 SELECTED DIFFERENCE
SCHEMES 167 5.2.1 THE FIRST ORDER UPWIND SCHEME 168 5.2.2 OTHER
WELL-KNOWN SCHEMES 172 5.3 CONSERVATIVE METHODS 174 5.3.1 BASIC
DEFINITIONS 175 5.3.2 GODUNOV S FIRST-ORDER UPWIND METHOD 177 5.3.3
GODUNOV S METHOD FOR BURGERS S EQUATION 180 5.3.4 CONSERVATIVE FORM OF
DIFFERENCE SCHEMES 184 5.4 UPWIND SCHEMES FOR LINEAR SYSTEMS 187 5.4.1
THE CIR SCHEME 188 5.4.2 GODUNOV S METHOD 190 5.5 SAMPLE NUMERICAL
RESULTS 193 5.5.1 LINEAR ADVECTION 193 5.5.2 THE INVISCID BURGERS
EQUATION 195 5.6 FORTRAN PROGRAM FOR GODUNOV S METHOD 196 6. THE METHOD
OF GODUNOV FOR NON-LINEAR SYSTEMS 213 6.1 BASES OF GODUNOV S METHOD 213
6.2 THE GODUNOV SCHEME 216 6.3 GODUNOV S METHOD FOR THE EULER EQUATIONS
218 6.3.1 EVALUATION OF THE INTERCELL FLUXES 219 6.3.2 TIME STEP SIZE
221 6.3.3 BOUNDARY CONDITIONS 222 6.4 NUMERICAL RESULTS AND DISCUSSION
225 6.4.1 NUMERICAL RESULTS FOR GODUNOV S METHOD 226 6.4.2 NUMERICAL
RESULTS FROM OTHER METHODS 228 XIV TABLE OF CONTENTS 7. RANDOM CHOICE
AND RELATED METHODS 237 7.1 INTRODUCTION 237 7.2 RCM ON A NON-STAGGERED
GRID 238 7.2.1 THE SCHEME FOR NON-LINEAR SYSTEMS 239 7.2.2 BOUNDARY
CONDITIONS AND THE TIME STEP SIZE 243 7.3 A RANDOM CHOICE SCHEME OF THE
LAX-FRIEDRICHS TYPE 244 7.3.1 REVIEW OF THE LAX-FRIEDRICHS SCHEME 244
7.3.2 THE SCHEME 245 7.4 THE RCM ON A STAGGERED GRID 246 7.4.1 THE
SCHEME FOR NON-LINEAR SYSTEMS 247 7.4.2 A DETERMINISTIC FIRST-ORDER
CENTRED SCHEME (FORCE) 248 7.4.3 ANALYSIS OF THE FORCE SCHEME 249 7.5
RANDOM NUMBERS 250 7.5.1 VAN DER CORPUT PSEUDO-RANDOM NUMBERS 250 7.5.2
STATISTICAL PROPERTIES 252 7.5.3 PROPAGATION OF A SINGLE SHOCK 253 7.6
NUMERICAL RESULTS 255 7.7 CONCLUDING REMARKS 257 8. FLUX VECTOR
SPLITTING METHODS 265 8.1 INTRODUCTION 265 8.2 THE FLUX VECTOR SPLITTING
APPROACH 266 8.2.1 UPWIND DIFFERENCING 266 8.2.2 THE FVS APPROACH 268
8.3 FVS FOR THE ISOTHERMAL EQUATIONS 270 8.3.1 SPLIT FLUXES 271 8.3.2
FVS NUMERICAL SCHEMES 272 8.4 FVS APPLIED TO THE EULER EQUATIONS 273
8.4.1 RECALLING THE EQUATIONS 273 8.4.2 THE STEGER-WARMING SPLITTING 275
8.4.3 THE VAN LEER SPLITTING 276 8.4.4 THE LIOU-STEFFEN SCHEME 278 8.5
NUMERICAL RESULTS 280 8.5.1 TESTS 280 8.5.2 RESULTS FOR TEST 1 280 8.5.3
RESULTS FOR TEST 2 281 8.5.4 RESULTS FOR TEST 3 281 8.5.5 RESULTS FOR
TEST 4 282 8.5.6 RESULTS FOR TEST 5 . 282 9. APPROXIMATE*STATE RIEMANN
SOLVERS 29 3 9.1 INTRODUCTION 293 9.2 THE RIEMANN PROBLEM AND THE
GODUNOV FLUX 294 9.2.1 TANGENTIAL VELOCITY COMPONENTS 296 9.2.2 SONIC
RAREFACTIONS 296 TABLE OF CONTENTS XV 9.3 PRIMITIVE VARIABLE RIEMANN
SOLVERS (PVRS) 297 9.4 APPROXIMATIONS BASED ON THE EXACT SOLVER 301
9.4.1 A TWO-RAREFACTION RIEMANN SOLVER (TRRS) 301 9.4.2 A TWO-SHOCK
RIEMANN SOLVER (TSRS) 303 9.5 ADAPTIVE RIEMANN SOLVERS 304 9.5.1 AN
ADAPTIVE ITERATIVE RIEMANN SOLVER (AIRS) 304 9.5.2 AN ADAPTIVE
NONITERATIVE RIEMANN SOLVER (ANRS) ... 305 9.6 NUMERICAL RESULTS 306 10.
THE HLL AND HLLC RIEMANN SOLVERS 315 10.1 THE RIEMANN PROBLEM AND THE
GODUNOV FLUX 316 10.2 THE RIEMANN PROBLEM AND INTEGRAL RELATIONS 317
10.3 THE HLL APPROXIMATE RIEMANN SOLVER 319 10.4 THE HLLC APPROXIMATE
RIEMANN SOLVER 321 10.5 WAVE-SPEED ESTIMATES 323 10.5.1 DIRECT WAVE
SPEED ESTIMATES 324 10.5.2 PRESSURE-VELOCITY BASED WAVE SPEED ESTIMATES
325 10.6 ALGORITHMS FOR INTERCELL FLUXES 327 10.6.1 THE HLL AND HLLC
FLUXES 327 10.6.2 THE RUSANOV FLUX 327 10.7 CONTACT WAVES AND PASSIVE
SCALARS 328 10.8- NUMERICAL RESULTS 329 10.9 CLOSING REMARKS AND
EXTENSIONS 331 11. THE RIEMANN SOLVER OF ROE 341 11.1 BASES OF THE ROE
APPROACH 342 11.1.1 THE EXACT RIEMANN PROBLEM AND THE GODUNOV FLUX.. 342
11.1.2. APPROXIMATE CONSERVATION LAWS 343 11.1.3 THE APPROXIMATE RIEMANN
PROBLEM AND THE INTERCELL FLUX 345 11.2 THE ORIGINAL ROE METHOD 347
11.2.1 THE ISOTHERMAL EQUATIONS 348 11.2.2 THE EULER EQUATIONS 350 11.3
THE ROE-PIKE METHOD 354 11.3.1 THE APPROACH 354 11.3.2 THE ISOTHERMAL
EQUATIONS 355 11.3.3 THE EULER EQUATIONS 359 11.4 AN ENTROPY FIX 362
11.4.1 THE ENTROPY PROBLEM 362 11.4.2 THE HARTEN-HYMAN ENTROPY FIX 363
11.4.3 THE SPEEDS U*, CL*L, A*R 366 11.5 NUMERICAL RESULTS AND
DISCUSSION 367 11.5.1 THE TESTS 367 11.5.2 THE RESULTS 368 11.6
EXTENSIONS 369 XVI TABLE OF CONTENTS 12. THE RIEMANN SOLVER OF OSHER 373
12.1 OSHER S SCHEME FOR A GENERAL SYSTEM 374 12.1.1 MATHEMATICAL BASES
374 12.1.2 OSHER S NUMERICAL FLUX 376 12.1.3 OSHER S FLUX FOR THE
SINGLE-WAVE CASE 377 12.1.4 OSHER S FLUX FOR THE INVISCID BURGERS
EQUATION 379 12.1.5 OSHER S FLUX FOR THE GENERAL CASE 380 12.2 OSHER S
FLUX FOR THE ISOTHERMAL EQUATIONS 381 12.2.1 OSHER S FLUX WITH
P-ORDERING 382 12.2.2 OSHER S FLUX WITH O-ORDERING 385 12.3 OSHER S
SCHEME FOR THE EULER EQUATIONS 388 12.3.1 OSHER S FLUX WITH P-ORDERING
389 12.3.2 OSHER S FLUX WITH O-ORDERING 391 12.3.3 REMARKS ON PATH
ORDERINGS 396 12.3.4 THE SPLIT THREE-DIMENSIONAL CASE 399 12.4 NUMERICAL
RESULTS AND DISCUSSION 400 12.5 EXTENSIONS 401 13. HIGH-ORDER AND TVD
METHODS FOR SCALAR EQUATIONS 409 13.1 INTRODUCTION 409 13.2 BASIC
PROPERTIES OF SELECTED SCHEMES 411 13.2.1 SELECTED SCHEMES ... 411
13.2.2 ACCURACY 413 13.2.3 STABILITY 414 13.3 WAF-TYPE HIGH ORDER
SCHEMES 416 13.3.1 THE BASIC WAF SCHEME 416 13.3.2 GENERALISATIONS OF
THE WAF SCHEME 419 13.4 MUSCL-TYPE HIGH-ORDER METHODS 422 13.4.1 DATA
RECONSTRUCTION 422 13.4.2 THE MUSCL-HANCOCK METHOD (MHM) 425 13.4.3 THE
PIECE-WISE LINEAR METHOD (PLM) 428 13.4.4 THE GENERALISED RIEMANN
PROBLEM (GRP) METHOD ... 430 13.4.5 SLOPE-LIMITER CENTRED (SLIC) SCHEMES
432 13.4.6 OTHER APPROACHES 435 13.4.7 SEMI-DISCRETE SCHEMES 435 13.4.8
IMPLICIT METHODS 436 13.5 MONOTONE SCHEMES AND ACCURACY 437 13.5.1
MONOTONE SCHEMES 437 13.5.2 A MOTIVATING EXAMPLE 440 13.5.3 MONOTONE
SCHEMES AND GODUNOV S THEOREM 442 13.5.4 SPURIOUS OSCILLATIONS AND HIGH
RESOLUTION 445 13.5.5 DATA COMPATIBILITY 446 13.6 TOTAL VARIATION
DIMINISHING (TVD) METHODS 448 13.6.1 THE TOTAL VARIATION 448 13.6.2 TVD
AND MONOTONICITY PRESERVING SCHEMES 449 TABLE OF CONTENTS XVII 13.7 FLUX
LIMITER METHODS 453 13.7.1 TVD VERSION OF THE WAF METHOD 453 13.7.2 THE
GENERAL FLUX-LIMITER APPROACH 460 13.7.3 TVD UPWIND FLUX LIMITER SCHEMES
465 13.7.4 TVD CENTRED FLUX LIMITER SCHEMES 470 13.8 SLOPE LIMITER
METHODS 476 13.8.1 TVD CONDITIONS 476 13.8.2 CONSTRUCTION OF TVD SLOPES
477 13.8.3 SLOPE LIMITERS 479 13.8.4 LIMITED SLOPES OBTAINED FROM FLUX
LIMITERS 481 13.9 EXTENSIONS OF TVD METHODS 482 13.9.1 TVD SCHEMES IN
THE PRESENCE OF SOURCE TERMS 482 13.9.2 TVD SCHEMES IN THE PRESENCE OF
DIFFUSION TERMS 483 13.10NUMERICAL RESULTS FOR LINEAR ADVECTION 484 14.
HIGH-ORDER AND TVD SCHEMES FOR NON-LINEAR SYSTEMS .. 489 14.1
INTRODUCTION 489 14.2 CFL AND BOUNDARY CONDITIONS 490 14.3 WEIGHTED
AVERAGE FLUX (WAF) SCHEMES 492 14.3.1 THE ORIGINAL VERSION OF WAF 492
14.3.2 A WEIGHTED AVERAGE STATE VERSION 494 14.3.3 RAREFACTIONS IN STATE
RIEMANN SOLVERS 495 14.3.4 TVD VERSION OF WAF SCHEMES 497 14.3.5 RIEMANN
SOLVERS 499 14.3.6 SUMMARY OF THE WAF METHOD 499 14.4 THE MUSCL-HANCOCK
SCHEME 500 14.4.1 THE BASIC SCHEME 500 14.4.2 A VARIANT OF THE SCHEME
502 14.4.3 TVD VERSION OF THE SCHEME 503 14.4.4 SUMMARY OF THE
MUSCL-HANCOCK METHOD 506 14.5 CENTRED TVD SCHEMES 507 14.5.1 REVIEW OF
THE FORCE FLUX 507 14.5.2 A FLUX LIMITER CENTRED (FLIC) SCHEME 508
14.5.3 A SLOPE LIMITER CENTRED (SLIC) SCHEME 510 14.6 PRIMITIVE-VARIABLE
SCHEMES 511 14.6.1 FORMULATION OF THE EQUATIONS AND PRIMITIVE SCHEMES .
511 14.6.2 A WAF-TYPE PRIMITIVE VARIABLE SCHEME 513 14.6.3 A
MUSCL-HANCOCK PRIMITIVE SCHEME 516 14.6.4 ADAPTIVE
PRIMITIVE-CONSERVATIVE SCHEMES 518 14.7 SOME NUMERICAL RESULTS 519
14.7.1 UPWIND TVD METHODS 519 14.7.2 CENTRED TVD METHODS 520 XVIII TABLE
OF CONTENTS 15. SPLITTING SCHEMES FOR PDES WITH SOURCE TERMS 527 15.1
INTRODUCTION 527 15.2 SPLITTING FOR A MODEL EQUATION 528 15.3 NUMERICAL
METHODS BASED ON SPLITTING 531 15.3.1 MODEL EQUATIONS 531 15.3.2 SCHEMES
FOR SYSTEMS 532 15.4 REMARKS ON ODE SOLVERS 533 15.4.1 FIRST-ORDER
SYSTEMS OF ODES 533 15.4.2 NUMERICAL METHODS 535 15.4.3 IMPLEMENTATION
DETAILS FOR SPLIT SCHEMES 536 15.5 CONCLUDING REMARKS 537 16. METHODS
FOR MULTI-DIMENSIONAL PDES 539 16.1 INTRODUCTION 539 16.2 DIMENSIONAL
SPLITTING 540 16.2.1 SPLITTING FOR A MODEL PROBLEM 540 16.2.2 SPLITTING
SCHEMES FOR TWO-DIMENSIONAL SYSTEMS 541 16.2.3 SPLITTING SCHEMES FOR
THREE-DIMENSIONAL SYSTEMS .... 543 16.3 PRACTICAL IMPLEMENTATION OF
SPLITTING SCHEMES IN THREE DI- MENSIONS 545 16.3.1 HANDLING THE SWEEPS
BY A SINGLE SUBROUTINE 545 16.3.2 CHOICE OF TIME STEP SIZE 547 16.3.3
THE INTERCELL FLUX AND THE TVD CONDITION 547 16.4 UNSPLIT FINITE VOLUME
METHODS 551 16.4.1 INTRODUCTORY CONCEPTS 551 16.4.2 ACCURACY AND
STABILITY OF MULTIDIMENSIONAL SCHEMES .. 554 16.5 A MUSCL-HANCOCK FINITE
VOLUME SCHEME 557 16.6 WAF-TYPE FINITE VOLUME SCHEMES 559 16.6.1
TWO-DIMENSIONAL LINEAR ADVECTION 559 16.6.2 THREE-DIMENSIONAL LINEAR
ADVECTION 563 16.6.3 SCHEMES FOR TWO-DIMENSIONAL NONLINEAR SYSTEMS ....
566 16.6.4 SCHEMES FOR THREE-DIMENSIONAL NONLINEAR SYSTEMS ... 569 16.7
NON-CARTESIAN GEOMETRIES 570 16.7.1 INTRODUCTION 570 16.7.2 GENERAL
DOMAINS AND COORDINATE TRANSFORMATION .... 571 16.7.3 THE FINITE VOLUME
METHOD FOR NON-CARTESIAN DOMAINS573 17. MULTIDIMENSIONAL TEST PROBLEMS
581 17.1 EXPLOSIONS AND IMPLOSIONS 581 17.1.1 EXPLOSION TEST IN
TWO-SPACE DIMENSIONS 582 17.1.2 IMPLOSION TEST IN TWO DIMENSIONS 585
17.1.3 EXPLOSION TEST IN THREE SPACE DIMENSIONS 586 17.2 SHOCK WAVE
REFLECTION FROM WEDGES 587 17.2.1 MACH NUMBER M S = 1.7 AND = 25 DEGREES
588 17.2.2 MACH NUMBER M S = 1.2 AND = 30 DEGREES 591 TABLE OF CONTENTS
XIX 18. CONCLUDING REMARKS 593 18.1 SUMMARY 593 18.2 EXTENSIONS AND
APPLICATIONS 594 18.2.1 SHALLOW WATER EQUATIONS 594 18.2.2 STEADY
SUPERSONIC EULER EQUATIONS 594 18.2.3 THE INCOMPRESSIBLE NAVIER-STOKES
EQUATIONS 595 18.2.4 THE COMPRESSIBLE NAVIER-STOKES EQUATIONS 595 18.2.5
COMPRESSIBLE MATERIALS 595 18.2.6 DETONATION WAVES 596 18.2.7 MULTIPHASE
FLOWS 596 18.2.8 MAGNETOHYDRODYNAMICS (MHD) 596 18.2.9 RELATIVISTIC GAS
DYNAMICS 597 18.2.10WAVES IN SOLIDS 597 18.3 NUMERICA 597 REFERENCES 599
INDEX 620
|
| any_adam_object | 1 |
| author | Toro, Elewterio F. 1946- |
| author_GND | (DE-588)115395210 |
| author_facet | Toro, Elewterio F. 1946- |
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| author_sort | Toro, Elewterio F. 1946- |
| author_variant | e f t ef eft |
| building | Verbundindex |
| bvnumber | BV012565289 |
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| callnumber-label | QA911 |
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| callnumber-search | QA911 |
| callnumber-sort | QA 3911 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 4000 |
| classification_tum | MTA 309f |
| ctrlnum | (OCoLC)723035491 (DE-599)BVBBV012565289 |
| dewey-full | 532/.05/015194 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.05/015194 |
| dewey-search | 532/.05/015194 |
| dewey-sort | 3532 15 515194 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 2. ed. |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV012565289 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:29:46Z |
| institution | BVB |
| isbn | 3540659668 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008532933 |
| oclc_num | 723035491 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-188 |
| owner_facet | DE-29T DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-188 |
| physical | XIX, 624 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| spelling | Toro, Elewterio F. 1946- Verfasser (DE-588)115395210 aut Riemann solvers and numerical methods for fluid dynamics a practical introduction Eleuterio F. Toro 2. ed. Berlin [u.a.] Springer 1999 XIX, 624 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 599 - 624 Fluides, Dynamique des - Informatique ram Datenverarbeitung Fluid dynamics Fluid dynamics Data processing Riemannsches Integral (DE-588)4049996-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Numerische Strömungssimulation (DE-588)4690080-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Numerische Strömungssimulation (DE-588)4690080-9 s DE-604 Strömungsmechanik (DE-588)4077970-1 s Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Riemannsches Integral (DE-588)4049996-0 s 3\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008532933&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Toro, Elewterio F. 1946- Riemann solvers and numerical methods for fluid dynamics a practical introduction Fluides, Dynamique des - Informatique ram Datenverarbeitung Fluid dynamics Fluid dynamics Data processing Riemannsches Integral (DE-588)4049996-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| subject_GND | (DE-588)4049996-0 (DE-588)4128130-5 (DE-588)4077970-1 (DE-588)4690080-9 (DE-588)4123623-3 |
| title | Riemann solvers and numerical methods for fluid dynamics a practical introduction |
| title_auth | Riemann solvers and numerical methods for fluid dynamics a practical introduction |
| title_exact_search | Riemann solvers and numerical methods for fluid dynamics a practical introduction |
| title_full | Riemann solvers and numerical methods for fluid dynamics a practical introduction Eleuterio F. Toro |
| title_fullStr | Riemann solvers and numerical methods for fluid dynamics a practical introduction Eleuterio F. Toro |
| title_full_unstemmed | Riemann solvers and numerical methods for fluid dynamics a practical introduction Eleuterio F. Toro |
| title_short | Riemann solvers and numerical methods for fluid dynamics |
| title_sort | riemann solvers and numerical methods for fluid dynamics a practical introduction |
| title_sub | a practical introduction |
| topic | Fluides, Dynamique des - Informatique ram Datenverarbeitung Fluid dynamics Fluid dynamics Data processing Riemannsches Integral (DE-588)4049996-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| topic_facet | Fluides, Dynamique des - Informatique Datenverarbeitung Fluid dynamics Fluid dynamics Data processing Riemannsches Integral Numerisches Verfahren Strömungsmechanik Numerische Strömungssimulation Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008532933&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT toroelewteriof riemannsolversandnumericalmethodsforfluiddynamicsapracticalintroduction |