Calculations of relativistic hydrodynamics are crucial to several areas of current research in the physics of supernovae and stellar collapse. This book provides an overview of the computational framework in which such calculations have been developed, with examples of applications to real physical systems. Beginning with the development of the equations and differencing schemes for special relativistic hydrodynamics, the book stresses the viability of the Euler-Lagrange approach to most astrophysical problems. It details aspects of solving the Einstein equations together with the fluid dynamics for various astrophysical systems in one, two and three dimensions.
Author(s): Wilson J.R., Mathews G.J.
Series: Cambridge Monographs on Mathematical Physics
Publisher: CUP
Year: 2003
Language: English
Pages: 233
Tags: Механика;Механика жидкостей и газов;Гидрогазодинамика;
Cover......Page 1
Frontmatter......Page 2
Contents......Page 8
Preface......Page 14
1 - Introduction......Page 18
1.1 Notation and convention......Page 19
1.2 General relativity......Page 20
1.3 (3+1) or ADM formalism......Page 25
References......Page 38
2.1 Perfect fluid energy momentum tensor......Page 40
2.2 Equation of motion......Page 42
2.3 Coordinate systems......Page 45
2.4 Difference equations: generalities......Page 46
2.5 Test problems......Page 65
2.6 Application to heavy ion collisions......Page 78
References......Page 90
3.1 General relativity......Page 92
3.2 General relativistic hydrodynamics......Page 93
3.3 Difference equations......Page 97
3.4 Multi-dimensional difference equations......Page 100
3.5 Grid calculation......Page 107
3.6 Artificial viscosity......Page 110
3.8 Time step......Page 113
References......Page 115
4.1 Planar cosmology......Page 116
4.2 Applications......Page 122
4.3 Spherical inhomogeneous cosmology......Page 128
References......Page 132
5.1 Collapse supernovae......Page 134
5.2 The physical model......Page 137
5.3 Numerical methods......Page 141
5.4 Neutrino evolution equation......Page 143
5.5 Neutrino--matter interactions......Page 149
5.6 Equation of state......Page 158
5.7 Convection......Page 168
5.8 Model of a 20 M[CIRCLED DOT OPERATOR] supernova explosion......Page 175
References......Page 179
6.1 Systems with a fixed metric......Page 182
6.2 Rotating stars......Page 187
6.3 Systems with a dynamic metric......Page 193
References......Page 196
7.1 The conformally flat approximation......Page 198
7.2 Conformally flat model for binary neutron stars......Page 200
7.3 Relativistic hydrodynamics......Page 210
7.4 Boundary conditions......Page 216
7.6 Results......Page 218
7.7 Solving the Einstein equation in three dimensions......Page 224
References......Page 226
Index......Page 231
