Elements of numerical relativity and relativistic hydrodynamics: from Einstein's equations to astrophysical simulations
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Edition: | 2. ed. |
| Series: | Lecture notes in physics
783 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 214 S. graph. Darst. |
| ISBN: | 9783642011634 9783642011641 3642011632 ebook 3642011640 |
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Record in the Search Index
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| adam_text | Titel: Elements of numerical relativity and relativistic hydrodynamics
Autor: Bona, Carles
Jahr: 2009
Contents
1 The 4D Spacetime........................................ 1
1.1 Spacetime geometry .................................... 1
1.1.1 The metric...................................... 1
1.1.2 General covariance ............................... 2
1.1.3 Covariant derivatives ............................. 3
1.1.4 Curvature....................................... 5
1.1.5 Symmetries of the curvature tensor................. 6
1.2 General covariant field equations......................... 7
1.2.1 The stress-energy tensor.......................... 7
1.2.2 Einstein s field equations.......................... 8
1.2.3 Structure of the field equations..................... 10
1.3 Einstein s equations solutions............................ 13
1.3.1 Symmetries: Lie derivatives........................ 13
1.3.2 Exact solutions .................................. 15
1.3.3 Analytical and numerical approximations............ 16
1.4 Harmonic formalism.................................... 18
1.4.1 The relaxed system............................... 19
1.4.2 Analytical and numerical applications............... 20
1.4.3 Harmonic coordinates............................. 22
References................................................. 24
2 The Evolution Formalism................................. 25
2.1 Space plus time decomposition........................... 25
2.1.1 A prelude: Maxwell equations...................... 26
2.1.2 Spacetime synchronization......................... 27
2.1.3 The Eulerian observers............................ 30
2.2 Einstein s equations decomposition....................... 32
2.2.1 The 3+1 form of the field equations ................ 32
2.2.2 3+1 Covariance.................................. 33
2.2.3 Generic space coordinates......................... 35
2.3 The evolution system................................... 38
xii Contents
2.3.1 Evolution and constraints ......................... 38
2.3.2 Constraints conservation.......................... 39
2.3.3 Evolution strategies............................... 40
2.4 Gravitational waves degrees of freedom.................... 42
2.4.1 Linearized field equations.......................... 42
2.4.2 Plane-wave analysis............................... 43
2.4.3 Gravitational waves and gauge effects............... 46
References................................................. 47
3 Free Evolution............................................ 49
3.1 The free evolution framework............................ 49
3.1.1 The ADM system................................ 49
3.1.2 Extended solution space........................... 50
3.1.3 Plane-wave analysis............................... 52
3.2 Robust stability test-bed................................ 55
3.2.1 Finite differences................................. 55
3.2.2 Numerical results................................. 58
3.3 Pseudo-hyperbolic systems............................... 60
3.3.1 Extra dynamical fields............................ 60
3.3.2 The BSSN system................................ 63
3.3.3 Plane-wave analysis............................... 65
3.4 Covariant formulations.................................. 67
3.4.1 The Z4 formalism................................ 67
3.4.2 The generalized harmonic formalism................ 69
3.4.3 Constraint-violation control........................ 70
3.5 The Z4 evolution system ................................ 71
3.5.1 3 + 1 Decomposition.............................. 71
3.5.2 Plane-wave analysis............................... 73
3.5.3 Symmetry breaking............................... 75
References................................................. 77
4 First-Order Hyperbolic Systems.......................... 79
4.1 First-order versions of second-order systems................ 79
4.1.1 Introducing extra first-order quantities.............. 79
4.1.2 Ordering ambiguities ............................. 81
4.1.3 First-order Z4 system (normal coordinates).......... 82
4.1.4 Symmetry breaking: the KST system............... 83
4.2 Hyperbolic systems..................................... 86
4.2.1 Weak and strong hyperbolicity..................... 86
4.2.2 ID Energy estimates.............................. 89
4.2.3 Symmetric-hyperbolic systems..................... 91
4.3 Generic space coordinates............................... 93
4.3.1 First-order fields................................. 93
4.3.2 Generalized harmonic formulations................. 96
4.3.3 First-order Z4 formalism.......................... 98
Contents
4.4 Boundary conditions.................................... 100
4.4.1 Algebraic boundary conditions..................... 101
4.4.2 Energy methods.................................. 103
4.4.3 Robust stability test.............................. 106
References................................................. 108
Numerical Methods.......................................109
5.1 Finite difference methods................................110
5.1.1 Accuracy and stability............................110
5.1.2 The method of lines..............................112
5.1.3 Artificial dissipation..............................113
5.1.4 The gauge waves test-bed.........................115
5.2 Finite volume methods..................................117
5.2.1 Systems of balance laws........................... 118
5.2.2 Weak solutions................................... 120
5.2.3 Flux formulae.................................... 123
5.2.4 High-resolution methods .......................... 126
5.2.5 The modified flux approach........................ 130
5.3 Simple CFD tests ...................................... 132
5.3.1 Advection equation...............................133
5.3.2 Burgers equation.................................135
5.3.3 Euler equations: Sod test..........................137
5.3.4 MHD equations: Orszag-Tang vortex...............138
References .................................................141
Black Hole Simulations...................................143
6.1 Black Hole initial data..................................143
6.1.1 Conformal metric decomposition...................146
6.1.2 Singular initial data: punctured black holes..........147
6.1.3 Regular initial data...............................149
6.2 Dynamical time slicing..................................155
6.2.1 Singularity avoidance.............................155
6.2.2 Limit surfaces....................................157
6.2.3 Gauge pathologies................................159
6.3 Numerical Black Hole milestones.........................160
6.3.1 Short-term simulations............................160
6.3.2 Long-term simulations............................166
6.3.3 Further developments.............................167
References.................................................^9
Matter Spacetimes .......................................171
7.1 Scalar fields............................................172
7.1.1 The Klein-Gordon equation .......................172
7.1.2 Boson stars initial data...........................i74
7.1.3 Evolution of a single boson star....................178
xiv Contents
7.2 Electromagnetic fields...................................179
7.2.1 Maxwell equations................................ 180
7.2.2 Electromagnetic potential......................... 181
7.2.3 The electromagnetic fields......................... 183
7.2.4 The electromagnetic stress-energy tensor............ 185
7.3 Hydrodynamics........................................ 185
7.3.1 Perfect fluids .................................... 186
7.3.2 The equation of state............................. 189
7.3.3 Neutron stars.................................... 192
7.4 Magnetohydrodynamics................................. 195
7.4.1 The MHD evolution equations.....................196
7.4.2 Generalized Ohm s law............................197
7.4.3 Ideal MHD......................................200
7.4.4 The force-free limit...............................204
7.5 Further developments...................................205
7.5.1 Boson stars collisions.............................205
7.5.2 Neutron stars collisions ...........................207
References.................................................209
Index.........................................................211
|
| any_adam_object | 1 |
| author | Bona, Carles Palenzuela-Luque, Carlos Bona-Casas, Carles |
| author_facet | Bona, Carles Palenzuela-Luque, Carlos Bona-Casas, Carles |
| author_role | aut aut aut |
| author_sort | Bona, Carles |
| author_variant | c b cb c p l cpl c b c cbc |
| building | Verbundindex |
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| callnumber-first | Q - Science |
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| dewey-full | 530.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
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| dewey-search | 530.11 |
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| discipline | Physik |
| edition | 2. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:51:50Z |
| institution | BVB |
| isbn | 9783642011634 9783642011641 3642011632 ebook 3642011640 |
| language | English |
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| physical | XIV, 214 S. graph. Darst. |
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| publisher | Springer |
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| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Bona, Carles Verfasser aut Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations C. Bona ; C. Palenzuela-Luque ; C. Bona-Casas 2. ed. Berlin [u.a.] Springer 2009 XIV, 214 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 783 Allgemeine Relativitätstheorie - Numerisches Verfahren Hydrodynamik - Relativistischer Effekt Magnetohydrodynamik - Relativistischer Effekt Mathematik Einstein field equations Numerical solutions Evolution equations Numerical solutions Relativity (Physics) Space and time Mathematics Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Relativistischer Effekt (DE-588)4129534-1 gnd rswk-swf Magnetohydrodynamik (DE-588)4130803-7 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Hydrodynamik (DE-588)4026302-2 s Relativistischer Effekt (DE-588)4129534-1 s Magnetohydrodynamik (DE-588)4130803-7 s Palenzuela-Luque, Carlos Verfasser aut Bona-Casas, Carles Verfasser aut Lecture notes in physics 783 (DE-604)BV000003166 783 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017994022&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bona, Carles Palenzuela-Luque, Carlos Bona-Casas, Carles Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations Lecture notes in physics Allgemeine Relativitätstheorie - Numerisches Verfahren Hydrodynamik - Relativistischer Effekt Magnetohydrodynamik - Relativistischer Effekt Mathematik Einstein field equations Numerical solutions Evolution equations Numerical solutions Relativity (Physics) Space and time Mathematics Hydrodynamik (DE-588)4026302-2 gnd Relativistischer Effekt (DE-588)4129534-1 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4026302-2 (DE-588)4129534-1 (DE-588)4130803-7 (DE-588)4112491-1 (DE-588)4128130-5 |
| title | Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations |
| title_auth | Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations |
| title_exact_search | Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations |
| title_full | Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations C. Bona ; C. Palenzuela-Luque ; C. Bona-Casas |
| title_fullStr | Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations C. Bona ; C. Palenzuela-Luque ; C. Bona-Casas |
| title_full_unstemmed | Elements of numerical relativity and relativistic hydrodynamics from Einstein's equations to astrophysical simulations C. Bona ; C. Palenzuela-Luque ; C. Bona-Casas |
| title_short | Elements of numerical relativity and relativistic hydrodynamics |
| title_sort | elements of numerical relativity and relativistic hydrodynamics from einstein s equations to astrophysical simulations |
| title_sub | from Einstein's equations to astrophysical simulations |
| topic | Allgemeine Relativitätstheorie - Numerisches Verfahren Hydrodynamik - Relativistischer Effekt Magnetohydrodynamik - Relativistischer Effekt Mathematik Einstein field equations Numerical solutions Evolution equations Numerical solutions Relativity (Physics) Space and time Mathematics Hydrodynamik (DE-588)4026302-2 gnd Relativistischer Effekt (DE-588)4129534-1 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Allgemeine Relativitätstheorie - Numerisches Verfahren Hydrodynamik - Relativistischer Effekt Magnetohydrodynamik - Relativistischer Effekt Mathematik Einstein field equations Numerical solutions Evolution equations Numerical solutions Relativity (Physics) Space and time Mathematics Hydrodynamik Relativistischer Effekt Magnetohydrodynamik Allgemeine Relativitätstheorie Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017994022&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT bonacarles elementsofnumericalrelativityandrelativistichydrodynamicsfromeinsteinsequationstoastrophysicalsimulations AT palenzuelaluquecarlos elementsofnumericalrelativityandrelativistichydrodynamicsfromeinsteinsequationstoastrophysicalsimulations AT bonacasascarles elementsofnumericalrelativityandrelativistichydrodynamicsfromeinsteinsequationstoastrophysicalsimulations |