Holdings: Riemann solvers and numerical methods for fluid dynamics

Riemann solvers and numerical methods for fluid dynamics: a practical introduction

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Bibliographic Details
Main Author:	Toro, Elewterio F. 1946- (Author)
Format:	Book
Language:	German
Published:	Berlin [u.a.] Springer 1999
Edition:	2. ed.
Subjects:	Fluides, Dynamique des - Informatique Datenverarbeitung Fluid dynamics Fluid dynamics > Data processing Riemannsches Integral Numerisches Verfahren Strömungsmechanik Numerische Strömungssimulation Lehrbuch
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 599 - 624
Physical Description:	XIX, 624 S. Ill., graph. Darst.
ISBN:	3540659668

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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. APPROXIMATESTATE 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, CLL, AR 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
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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
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physical	XIX, 624 S. Ill., graph. Darst.
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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

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