A New Spherically Symmetric General Relativistic Hydrodynamical Code

Romero, Javier; Ibáñez, Javier; Martí, Juan José Ibàñez; Miralles, J. A.

doi:10.1086/177198

Cited by 88 publications

(139 citation statements)

References 39 publications

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“…We follow [30,34] which formulate the 3 + 1 GR curvature and hydrodynamics equations in RGPS coordinates. In these coordinates and in spherical symmetry, the shift vector vanishes and the metric is diagonal and closely resembles the Schwarzschild metric.…”

Section: Curvature Equations In 1d Rgpsmentioning

confidence: 99%

A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes

O’Connor

Ott

2010

Class. Quantum Grav.

275

318

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We present the new open-source spherically symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero-Ibáñez-Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We present an array of standard test calculations and also show how simple analytic equations of state in combination with presupernova models from stellar evolutionary calculations can be used to study qualitative aspects of black hole formation in failing rotating core-collapse supernovae. In addition, we present a simulation with microphysical equations of state and neutrino leakage/heating of a failing corecollapse supernova and black hole formation in a presupernova model of a 40 M zero-age main-sequence star. We find good agreement on the time of black hole formation (within 20%) and last stable protoneutron star mass (within 10%) with predictions from simulations with full Boltzmann neutrino radiation hydrodynamics.

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Section: Curvature Equations In 1d Rgpsmentioning

confidence: 99%

A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes

O’Connor

Ott

2010

Class. Quantum Grav.

275

318

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“…With the help of Eqs. (3) and (6), the time derivative of 1/D leads to the continuity equation (15). An energy equation is obtained by taking the time derivative of specific total energy 1 + τ and substituting Eq.…”

Section: Conservative Einstein Equationsmentioning

confidence: 99%

“…We will first point out their relation to the general relativistic jump conditions at a shock front and then derive a consistent incorporation of artificial viscosity in Eqs. (15)(16)(17)(18)(19)(20). In a second and third part, we investigate the general relativistic Boltzmann equation with two different natural descriptions of the momentum phase space for the radiation particles.…”

Section: Conservative Einstein Equationsmentioning

confidence: 99%

“…A conservation law can then be integrated over an infinitesimal range around the shock front, containing rest mass ∆a L on the left-hand side and ∆a R on the right-hand side of the shock at position a s . For example, the continuity equation (15) …”

Section: Shock Waves and Artificial Viscositymentioning

confidence: 99%

“…The computational domain stays outside the apparent horizon for all times. This time slicing was implemented by Romero et al [15] in orthogonal coordinates. Schinder et al [16] found an interesting compromise by introducing nonzero shift vectors to get comoving coordinates in polar slicing.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Conservative general relativistic radiation hydrodynamics in spherical symmetry and comoving coordinates

2001

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The description of general relativistic radiation hydrodynamics in spherical symmetry is presented in natural coordinate choices. For hydrodynamics, comoving coordinates are chosen and the momentum phase space for the radiation particles is described in comoving frame four momenta. We also investigate a description of the momentum phase space in terms of particle impact parameter and energy at infinity and derive a simple approximation to the general relativistic Boltzmann equation. Further developed are, however, the exact equations in comoving coordinates since the description of the interaction between matter and radiation particles is best described in the closely related orthonormal basis comoving with the fluid elements. We achieve a conservative and concise formulation of radiation hydrodynamics that is well suited for numerical implementation by a variety of methods. The contribution of radiation to the general relativistic jump conditions at shock fronts is discussed and artificial viscosity is consistently included in the derivations in order to support approaches relying on this option.

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Review of numerical special relativistic hydrodynamics

Odyck

2004

Numerical Methods in Fluids

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SUMMARYThis paper gives an overview of numerical methods for special relativistic hydrodynamics (SRHD). First, a short summary of special relativity is given. Next, the SRHD equations are introduced. The exact solution for the SRHD Riemann problem is described. This solution is used in a Godunov scheme to compute solutions for two test problems. A third test problem is used to show non-convergent behaviour of the numerical solution at the location of the contact discontinuity. Finally, a short description of numerical methods used so far in SRHD is given.

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A New Spherically Symmetric General Relativistic Hydrodynamical Code

Cited by 88 publications

References 39 publications

A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes

A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes

Conservative general relativistic radiation hydrodynamics in spherical symmetry and comoving coordinates

Review of numerical special relativistic hydrodynamics

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