### Abstract

An implicit Lagrangian hydrodynamics code for general relativistic spherical collapse is presented. This scheme is based on an approximate linearized Riemann solver (Roe-type scheme) and needs no artificial viscosity. This code is aimed especially at the calculation of the late phase of collapse-driven supernovae and the nascent neutron star, where there is a remarkable contrast between the dynamical timescale of the proto-neutron star and the diffusion timescale of neutrinos, without such severe limitation of the Courant condition at the center of the neutron star. Several standard test calculations have been done, and their results show the following: (1) This code captures the shock wave accurately, although some erroneous jumps of specific internal energy are found at the contact discontinuity in the shock tube problems. (2) The scheme shows no instability even if we choose the Courant number larger than 1. (3) However, the Courant number should be kept below ∼0.2 at the shock position, so that the shock can be resolved with a few meshes. (4) The scheme reproduces the well-known analytic solutions to the point blast explosion, the gravitational collapse of the uniform gas with y = 4/3, and the general relativistic collapse of uniform dust. In addition, what is more important, calculations of hydrostatic configurations and the onset of radial instability, a preliminary neutrino transport in a proto-neutron star, and adiabatic collapses of a stellar core have also been done in order to show the performance of the code in the context of the collapse-driven supernovae. It is found that the time step can be extended far beyond the Courant limitation at the center of the neutron star, which fact is crucially significant for the purpose of this project. The details of the scheme and the results of these test calculations are discussed.

Original language | English |
---|---|

Pages (from-to) | 720-739 |

Number of pages | 20 |

Journal | Astrophysical Journal |

Volume | 475 |

Issue number | 2 PART I |

DOIs | |

Publication status | Published - 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Hydrodynamics
- Methods: numerical
- Relativity
- Stars: interiors
- Supernovae: general

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

**An implicit lagrangian code for spherically symmetric general relativistic hydrodynamics with an approximate riemann solver.** / Yamada, Shoichi.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 475, no. 2 PART I, pp. 720-739. https://doi.org/10.1086/303548

}

TY - JOUR

T1 - An implicit lagrangian code for spherically symmetric general relativistic hydrodynamics with an approximate riemann solver

AU - Yamada, Shoichi

PY - 1997

Y1 - 1997

N2 - An implicit Lagrangian hydrodynamics code for general relativistic spherical collapse is presented. This scheme is based on an approximate linearized Riemann solver (Roe-type scheme) and needs no artificial viscosity. This code is aimed especially at the calculation of the late phase of collapse-driven supernovae and the nascent neutron star, where there is a remarkable contrast between the dynamical timescale of the proto-neutron star and the diffusion timescale of neutrinos, without such severe limitation of the Courant condition at the center of the neutron star. Several standard test calculations have been done, and their results show the following: (1) This code captures the shock wave accurately, although some erroneous jumps of specific internal energy are found at the contact discontinuity in the shock tube problems. (2) The scheme shows no instability even if we choose the Courant number larger than 1. (3) However, the Courant number should be kept below ∼0.2 at the shock position, so that the shock can be resolved with a few meshes. (4) The scheme reproduces the well-known analytic solutions to the point blast explosion, the gravitational collapse of the uniform gas with y = 4/3, and the general relativistic collapse of uniform dust. In addition, what is more important, calculations of hydrostatic configurations and the onset of radial instability, a preliminary neutrino transport in a proto-neutron star, and adiabatic collapses of a stellar core have also been done in order to show the performance of the code in the context of the collapse-driven supernovae. It is found that the time step can be extended far beyond the Courant limitation at the center of the neutron star, which fact is crucially significant for the purpose of this project. The details of the scheme and the results of these test calculations are discussed.

AB - An implicit Lagrangian hydrodynamics code for general relativistic spherical collapse is presented. This scheme is based on an approximate linearized Riemann solver (Roe-type scheme) and needs no artificial viscosity. This code is aimed especially at the calculation of the late phase of collapse-driven supernovae and the nascent neutron star, where there is a remarkable contrast between the dynamical timescale of the proto-neutron star and the diffusion timescale of neutrinos, without such severe limitation of the Courant condition at the center of the neutron star. Several standard test calculations have been done, and their results show the following: (1) This code captures the shock wave accurately, although some erroneous jumps of specific internal energy are found at the contact discontinuity in the shock tube problems. (2) The scheme shows no instability even if we choose the Courant number larger than 1. (3) However, the Courant number should be kept below ∼0.2 at the shock position, so that the shock can be resolved with a few meshes. (4) The scheme reproduces the well-known analytic solutions to the point blast explosion, the gravitational collapse of the uniform gas with y = 4/3, and the general relativistic collapse of uniform dust. In addition, what is more important, calculations of hydrostatic configurations and the onset of radial instability, a preliminary neutrino transport in a proto-neutron star, and adiabatic collapses of a stellar core have also been done in order to show the performance of the code in the context of the collapse-driven supernovae. It is found that the time step can be extended far beyond the Courant limitation at the center of the neutron star, which fact is crucially significant for the purpose of this project. The details of the scheme and the results of these test calculations are discussed.

KW - Hydrodynamics

KW - Methods: numerical

KW - Relativity

KW - Stars: interiors

KW - Supernovae: general

UR - http://www.scopus.com/inward/record.url?scp=21744462534&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21744462534&partnerID=8YFLogxK

U2 - 10.1086/303548

DO - 10.1086/303548

M3 - Article

VL - 475

SP - 720

EP - 739

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2 PART I

ER -