Computational methods for astrophysical fluid flow: lecture notes 1997
Gespeichert in:
| Format: | Tagungsbericht Buch |
|---|---|
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 508 S. Ill., graph. Darst. |
| ISBN: | 9783642084126 3540644482 |
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Datensatz im Suchindex
| _version_ | 1804126630695665664 |
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| adam_text | R. J. LEVEQUE D. MIHALAS E.A.DORFI E. MIILLER COMPUTATIONAL METHODS FOR
ASTROPHYSICAL FLUID FLOW SAAS-FEE ADVANCED COURSE 27 LECTURE NOTES 1997
SWISS SOCIETY FOR ASTROPHYSICS AND ASTRONOMY EDITED BY O. STEINER AND A.
GAUTSCHY WITH 124 FIGURES SPRINGER TABLE OF CONTENTS NONLINEAR
CONSERVATION LAWS AND FINITE VOLUME METHODS RANDALL J. LEVEQUE 1 1.
INTRODUCTION 1 1.1 SOFTWARE 3 1.2 NOTATION 4 1.3 CLASSIFICATION OF
DIFFERENTIAL EQUATIONS 5 2. DERIVATION OF CONSERVATION LAWS 8 2.1 THE
EULER EQUATIONS OF GAS DYNAMICS 10 2.2 DISSIPATIVE FLUXES 11 2.3 SOURCE
TERMS 11 2.4 RADIATIVE TRANSFER AND ISOTHERMAL EQUATIONS 12 2.5
MULTI-DIMENSIONAL CONSERVATION LAWS 14 2.6 THE SHOCK TUBE PROBLEM 15 3.
MATHEMATICAL THEORY OF HYPERBOLIC SYSTEMS 22 3.1 SCALAR EQUATIONS 22 3.2
LINEAR HYPERBOLIC SYSTEMS 27 3.3 NONLINEAR SYSTEMS 32 3.4 THE RIEMANN
PROBLEM FOR THE EULER EQUATIONS 40 4. NUMERICAL METHODS IN ONE DIMENSION
43 4.1 FINITE DIFFERENCE THEORY 43 4.2 FINITE VOLUME METHODS 52 4.3
IMPORTANCE OF CONSERVATION FORM * INCORRECT SHOCK SPEEDS .. 55 4.4
NUMERICAL FLUX FUNCTIONS 56 4.5 GODUNOV S METHOD 56 4.6 APPROXIMATE
RIEMANN SOLVERS 60 4.7 HIGH-RESOLUTION METHODS 64 4.8 OTHER APPROACHES
78 4.9 BOUNDARY CONDITIONS 82 5. SOURCE TERMS AND FRACTIONAL STEPS 84
5.1 UNSPLIT METHODSV. 85 5.2 FRACTIONAL STEP METHODS 86 5.3 GENERAL
FORMULATION OF FRACTIONAL STEP METHODS 87 5.4 STIFF SOURCE TERMS 90 VIII
TABLE OF CONTENTS 5.5 QUASI-STATIONARY FLOW AND GRAVITY 96 6.
MULTI-DIMENSIONAL PROBLEMS 101 6.1 DIMENSIONAL SPLITTING 103 6.2
MULTI-DIMENSIONAL FINITE VOLUME METHODS 103 6.3 GRIDS AND ADAPTIVE
REFINEMENT 104 7. COMPUTATIONAL DIFFICULTIES ILL 7.1 LOW-DENSITY FLOWS
ILL 7.2 DISCRETE SHOCKS AND VISCOUS PROFILES 112 7.3 START-UP ERRORS 113
7.4 WALL HEATING 115 7.5 SLOW-MOVING SHOCKS 115 7.6 GRID ORIENTATION
EFFECTS 116 7.7 GRID-ALIGNED SHOCKS 116 8. MAGNETOHYDRODYNAMICS 118 8.1
THE MHD EQUATIONS 119 8.2 ONE-DIMENSIONAL MHD 121 8.3 SOLVING THE
RIEMANN PROBLEM 125 8.4 NONSTRICT HYPERBOLICITY 125 8.5 STIFFNESS 127
8.6 THE DIVERGENCE OF B , 128 8.7 RIEMANN PROBLEMS IN MULTI-DIMENSIONAL
MHD 130 8.8 STAGGERED GRIDS 131 8.9 THE 8-WAVE RIEMANN SOLVER 132 9.
RELATIVISTIC HYDRODYNAMICS 132 9.1 CONSERVATION LAWS IN SPACETIME 133
9.2 THE CONTINUITY EQUATION 135 9.3 THE 4-MOMENTUM OF A PARTICLE 136 9.4
THE STRESS-ENERGY TENSOR 137 9.5 FINITE VOLUME METHODS 139 9.6
MULTI-DIMENSIONAL RELATIVISTIC FLOW 141 9.-7~ GRAVITATION AND GENERAL
RELATIVITY 142 REFERENCES 148 RADIATION HYDRODYNAMICS DIMITRI MIHALAS
161 1. BASIC RADIATION THEORY 161 1.1 SPECIFIC INTENSITY 161 1.2 PHOTON
NUMBER DENSITY 161 1.3 PHOTON DISTRIBUTION FUNCTION 162 1.4 MEAN
INTENSITY 162 1.5 RADIATION ENERGY DENSITY 162 1.6 RADIATION ENERGY FLUX
163 1.7 RADIATION MOMENTUM DENSITY 163 1.8 RADIATION STRESS TENSOR
(RADIATION PRESSURE TENSOR) 164 TABLE OF CONTENTS IX 1.9 THERMAL
RADIATION 166 1.10 THERMODYNAMICS OF THERMAL RADIATION AND A PERFECT GAS
.... 168 2. THE TRANSFER EQUATION 169 2.1 ABSORPTION, EMISSION, AND
SCATTERING 169 2.2 THE EQUATION OF TRANSFER 171 2.3 MOMENTS OF THE
TRANSFER EQUATION 174 3. LORENTZ TRANSFORMATION OF THE TRANSFER EQUATION
178 3.1 LORENTZ TRANSFORMATION OF THE PHOTON 4-MOMENTUM 178 3.2 LORENTZ
TRANSFORMATION OF THE SPECIFIC INTENSITY, OPACITY, AND EMISSIVITY 180
3.3 LORENTZ TRANSFORMATION OF THE RADIATION STRESS ENERGY TENSOR. 182
3.4 THE RADIATION 4-FORCE DENSITY VECTOR 184 3.5 COVARIANT FORM OF THE
TRANSFER EQUATION 185 4. INERTIAL-FRAME EQUATIONS OF RADIATION
HYDRODYNAMICS 188 4.1 INERTIAL-FRAME RADIATION EQUATIONS 188 4.2
INERTIAL-FRAME EQUATIONS OF RADIATION HYDRODYNAMICS 194 5.
COMOVING-FRAME EQUATION OF TRANSFER 199 5.1 SPECIAL RELATIVISTIC
DERIVATION (D. MIHALAS) 199 5.2 CONSISTENCY BETWEEN COMOVING-FRAME AND
INERTIAL-FRAME EQUATIONS 205 5.3 NONINERTIAL FRAME DERIVATION (J.I.
CASTOR) 206 5.4 ANALYSIS OF O(V/C) TERMS 210 6. LAGRANGIAN EQUATIONS OF
RADIATION HYDRODYNAMICS 211 6.1 MOMENTUM EQUATION 211 6.2 GAS ENERGY
EQUATION 212 6.3 FIRST LAW OF THERMODYNAMICS FOR THE RADIATION FIELD 213
6.4 FIRST LAW OF THERMODYNAMICS FOR THE RADIATING FLUID 213 6.5
MECHANICAL ENERGY EQUATION 214 6.6 TOTAL ENERGY EQUATION 214 6.7
CONSISTENCY OF DIFFERENT FORMS OF THE RADIATING-FLUID ENERGY AND
MOMENTUM EQUATIONS .,............. 216 6.8 CONSISTENCY OF INERTIAL-FRAME
AND COMOVING-FRAME RADIATION ENERGY AND MOMENTUM EQUATIONS 217 7.
RADIATION DIFFUSION 219 7.1 RADIATION DIFFUSION 219 7.2 NONEQUILIBRIUM
DIFFUSION 226 7.3 THE PROBLEM OF FLUX LIMITING 231 8. SHOCK PROPAGATION:
NUMERICAL METHODS 234 8.1 ACOUSTIC WAVES 234 8.2 NUMERICAL STABILITY ,
235 8.3 SYSTEMS OF EQUATIONS 236 8.4 IMPLICATIONS OF SHOCKDEVELOPMENT
238 8.5 IMPLICATIONS OF DIFFUSIVE ENERGY TRANSPORT 239 8.6 ILLUSTRATIVE
EXAMPLE 241 X TABLE OF CONTENTS 9. NUMERICAL RADIATION HYDRODYNAMICS 245
9.1 RADIATING FLUID ENERGY AND MOMENTUM EQUATIONS 245 9.2 COMPUTATIONAL
STRATEGY 247 9.3 ENERGY CONSERVATION 249 9.4 FORMAL SOLUTION 249 9.5
MULTIGROUP EQUATIONS 251 9.6 AN ASTROPHYSICAL EXAMPLE 251 10.
ADAPTIVE-GRID RADIATION HYDRODYNAMICS 254 10.1 FRONT FITTING 254 10.2
ARTIFICIAL DISSIPATION 255 10.3 THE ADAPTIVE GRID 255 10.4 THE TITAN
CODE 259 REFERENCES 260 RADIATION HYDRODYNAMICS: NUMERICAL ASPECTS AND
APPLICATIONS ERNST A. DORFI 263 1. INTRODUCTION 263 1.1 GENERAL REMARKS
ON THE NUMERICAL METHOD 263 1.2 TIME SCALES 264 1.3 LENGTH SCALES : 264
1.4 INTERACTION BETWEEN MATTER AND RADIATION 265 1.5 MOVING FRONTS 266
2. BASIC EQUATIONS 267 2.1 RADIATION HYDRODYNAMICS (RHD) 267 2.2
COUPLING TERMS :..-... 269 2.3 CLOSURE CONDITION 269 2.4 OPACITY * 271
2.5 EQUATION OF STATE 272 2.6 TRANSPORT THEOREM 274 3. ^SOLUTION
STRATEGY 275 3.1 INTEGRAL FORM OF THE RHD EQUATIONS 275 3.2 SYMBOLIC
NOTATION 277 3.3 MOVING COORDINATES 277 3.4 IMPLICIT DISCRETIZATION 277
3.5 TIME-CENTERING 279 3.6 ADAPTIVE RHD EQUATIONS 280 3.7 DISCRETIZATION
OF GRADIENTS AND DIVERGENCE TERMS ............ 280 3.8 DIFFUSION . 281
3.9 ADVECTION 282 3.10 INITIAL CONDITIONS 283 3.11 BOUNDARY CONDITIONS .
284 3.12 ARTIFICIAL VISCOSITY 285 3.13 DISCRETE RHD EQUATIONS ..... 286
TABLE OF CONTENTS XI 3.14 RADIATIVE CLOSURE CONDITION 288 3.15 RADIATIVE
BOUNDARY CONDITIONS 290 3.16 EDDINGTON FACTOR 290 4. ADAPTIVE GRIDS 291
4.1 BASIC GRID PROPERTIES 292 4.2 DESIRED RESOLUTION 292 4.3 SPATIAL AND
TEMPORAL SMOOTHING 293 4.4 GRID EQUATION 294 4.5 GRID BOUNDARY
CONDITIONS 295 4.6 GRID MOTION 296 4.7 REMARKS ON THE GRID EQUATION 296
4.8 FIRST EXAMPLE: SIMPLE TEST FUNCTION 297 4.9 SECOND EXAMPLE: SHOCK
TUBE PROBLEM 298 4.10 INITIAL GRID DISTRIBUTIONS 303 5. FURTHER
COMPUTATIONAL NEEDS 307 5.1 RATIONAL SPLINE INTERPOLATION 307 5.2
CPU-TIME REQUIREMENTS 308 5.3 ITERATION PROCEDURE AND MATRIX INVERSION
309 5.4 STRUCTURE OF THE JACOBI MATRIX 310 5.5 TIME-STEP CONTROL 312 6.
COMPUTATIONAL EXAMPLES 312 6.1 EVOLUTION OF SUPERNOVA REMNANTS (SNRS)
312 6.2 NONLINEAR STELLAR PULSATIONS 319 6.3 PROTOSTELLAR COLLAPSE 326
6.4 DUST-DRIVEN WINDS 329 6.5 RADIATIVE TRANSFER 332 7. DISCUSSION 334
7.1 INTERNAL ACCURACY 334 7.2 PROBLEMS 335 7.3 ADVANTAGES AND
DISADVANTAGES OF THE IMPLICIT FORMULATION 336 7.4 NUCLEAR AND CHEMICAL
NETWORKS AND CONVECTION 337 7.5 MULTIDIMENSIONAL VERSIONS 338 7.6
IMPROVEMENTS AND FURTHER RECOMMENDATIONS 338 REFERENCES 340 SIMULATION
OF ASTROPHYSICAL FLUID FLOW EWALD MULLER 343 1. INTRODUCTION 343 2.
SIMULATIONS: A LINK BETWEEN OBSERVATION AND THEORY 344 2.1 PROCEDURE AND
RESOURCES 346 2.2 SOME BASIC ISSUES 348 3. SIMULATIONS OF CORE COLLAPSE
SUPERNOVAE 353 3.1 SUPERNOVA OBSERVATIONS 353 3.2 PHYSICS OF SPHERICAL
CORE COLLAPSE 360 XII TABLE OF CONTENTS 3.3 OBSERVATIONS DEMANDING
NONSPHERICAL MODELS 371 3.4 RAYLEIGH-TAYLOR INSTABILITIES IN SUPERNOVA
ENVELOPES 374 3.5 SIMULATIONS OF RT INSTABILITIES IN SUPERNOVA ENVELOPES
375 3.6 NEUTRINO DRIVEN CONVECTIVE INSTABILITIES 377 3.7 ROTATIONAL CORE
COLLAPSE 382 3.8 GRAVITATIONAL WAVE SIGNATURE OF CORE COLLAPSE
SUPERNOVAE .... 392 4. HYDRODYNAMICS AND THERMONUCLEAR BURNING 405 4.1
TIME SCALES 406 4.2 TYPES OF BURNING 408 4.3 NUCLEAR REACTION NETWORKS
419 4.4 COUPLING REACTION NETWORKS AND HYDRODYNAMICS 425 4.5 SOME
INSTRUCTIVE NUMERICAL EXPERIMENTS 431 5. SIMULATION OF ASTROPHYSICAL
JETS 437 5.1 OBSERVATIONS OF EXTRAGALACTIC JETS 439 5.2 NEWTONIAN
HYDRODYNAMIC SIMULATIONS OF EXTRAGALACTIC JETS ... 443 . 5.3 MORPHOLOGY
AND DYNAMICS 445 5.4 RELATIVISTIC SIMULATIONS 451 5.5 MORPHOLOGY AND
DYNAMICS OF RELATIVISTIC JETS 456 5.6 LONG TERM EVOLUTION OF
RELATIVISTIC JETS 460 5.7 SIMULATION OF PARSEC-SCALE JETS 462 6.
SMOOTHED PARTICLE HYDRODYNAMICS 463 6.1 THE SPH FORMALISM 464 6.2
SELF-GRAVITY 467 6.3 VARIABLE SMOOTHING LENGTH 470 6.4 TIME INTEGRATION,
INITIAL MODEL 472 6.5 COMPUTATIONAL ASPECTS 473 6.6 HOW DISSIPATIVE IS
SPH? 474 6.7 HOW WELL DOES SPH TREAT SHOCKS? 476 REFERENCES 480 INDEX
495
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| indexdate | 2024-07-09T18:20:31Z |
| institution | BVB |
| institution_GND | (DE-588)600073-3 (DE-588)2170772-8 |
| isbn | 9783642084126 3540644482 |
| language | German |
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| spelling | Computational methods for astrophysical fluid flow lecture notes 1997 Saas Fee Advanced Course 27. R. J. LeVeque ... Swiss Society for Astrophysics and Astronomy. Ed. by O. Steiner ... Berlin [u.a.] Springer 1998 XIV, 508 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Astrophysik (DE-588)4003326-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1997 Les Diablerets gnd-content Astrophysik (DE-588)4003326-0 s Hydrodynamik (DE-588)4026302-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 LeVeque, Randall J. 1955- Sonstige (DE-588)112053688 oth Steiner, Oskar Sonstige oth Schweizerische Gesellschaft für Astrophysik und Astronomie Sonstige (DE-588)600073-3 oth Saas Fee Advanced Course 27 1997 Les Diablerets Sonstige (DE-588)2170772-8 oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008144634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Computational methods for astrophysical fluid flow lecture notes 1997 Numerisches Verfahren (DE-588)4128130-5 gnd Hydrodynamik (DE-588)4026302-2 gnd Astrophysik (DE-588)4003326-0 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4026302-2 (DE-588)4003326-0 (DE-588)1071861417 |
| title | Computational methods for astrophysical fluid flow lecture notes 1997 |
| title_auth | Computational methods for astrophysical fluid flow lecture notes 1997 |
| title_exact_search | Computational methods for astrophysical fluid flow lecture notes 1997 |
| title_full | Computational methods for astrophysical fluid flow lecture notes 1997 Saas Fee Advanced Course 27. R. J. LeVeque ... Swiss Society for Astrophysics and Astronomy. Ed. by O. Steiner ... |
| title_fullStr | Computational methods for astrophysical fluid flow lecture notes 1997 Saas Fee Advanced Course 27. R. J. LeVeque ... Swiss Society for Astrophysics and Astronomy. Ed. by O. Steiner ... |
| title_full_unstemmed | Computational methods for astrophysical fluid flow lecture notes 1997 Saas Fee Advanced Course 27. R. J. LeVeque ... Swiss Society for Astrophysics and Astronomy. Ed. by O. Steiner ... |
| title_short | Computational methods for astrophysical fluid flow |
| title_sort | computational methods for astrophysical fluid flow lecture notes 1997 |
| title_sub | lecture notes 1997 |
| topic | Numerisches Verfahren (DE-588)4128130-5 gnd Hydrodynamik (DE-588)4026302-2 gnd Astrophysik (DE-588)4003326-0 gnd |
| topic_facet | Numerisches Verfahren Hydrodynamik Astrophysik Konferenzschrift 1997 Les Diablerets |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008144634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT levequerandallj computationalmethodsforastrophysicalfluidflowlecturenotes1997 AT steineroskar computationalmethodsforastrophysicalfluidflowlecturenotes1997 AT schweizerischegesellschaftfurastrophysikundastronomie computationalmethodsforastrophysicalfluidflowlecturenotes1997 AT saasfeeadvancedcourselesdiablerets computationalmethodsforastrophysicalfluidflowlecturenotes1997 |