106 research outputs found
An Implicit Lagrangean Code for Spherically Symmetric General Relativistic Hydrodynamics with an Approximate Riemann Solver
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). 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 time
scale of the proto-neutron star and the diffusion time scale of neutrinos,
without such severe limitation of the Courant condition at the center of the
neutron star. Several standard test calculations have been done. Two other
adiabatic simulations have also been done in order to test 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. The details of the scheme and the results of these test
calculations are discussed.Comment: AASTeX v4.0, 24 pages, 13 figures on request from
[email protected], submitted to Ap
Equation of State in Numerical Relativistic Hydrodynamics
Relativistic temperature of gas raises the issue of the equation of state
(EoS) in relativistic hydrodynamics. We study the EoS for numerical
relativistic hydrodynamics, and propose a new EoS that is simple and yet
approximates very closely the EoS of the single-component perfect gas in
relativistic regime. We also discuss the calculation of primitive variables
from conservative ones for the EoS's considered in the paper, and present the
eigenstructure of relativistic hydrodynamics for a general EoS, in a way that
they can be used to build numerical codes. Tests with a code based on the Total
Variation Diminishing (TVD) scheme are presented to highlight the differences
induced by different EoS's.Comment: To appear in the ApJS September 2006, v166n1 issue. Pdf with full
resolution figures can be downloaded from
http://canopus.cnu.ac.kr/ryu/ryuetal.pd
Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics
Conservative numerical schemes for general relativistic magnetohydrodynamics
(GRMHD) require a method for transforming between ``conserved'' variables such
as momentum and energy density and ``primitive'' variables such as rest-mass
density, internal energy, and components of the four-velocity. The forward
transformation (primitive to conserved) has a closed-form solution, but the
inverse transformation (conserved to primitive) requires the solution of a set
of five nonlinear equations. Here we discuss the mathematical properties of the
inverse transformation and present six numerical methods for performing the
inversion. The first method solves the full set of five nonlinear equations
directly using a Newton-Raphson scheme and a guess from the previous timestep.
The other methods reduce the five nonlinear equations to either one or two
nonlinear equations that are solved numerically. Comparisons between the
methods are made using a survey over phase space, a two-dimensional explosion
problem, and a general relativistic MHD accretion disk simulation. The run-time
of the methods is also examined. Code implementing the schemes is available for
download on the web.Comment: Accepted to ApJ, 33 pages, 8 figures (color and greyscale), 1
machine-readable table (tab2.txt), code available at
http://rainman.astro.uiuc.edu/codelib, a high-resolution and full-color PDF
version is located at
http://rainman.astro.uiuc.edu/codelib/codes/pvs_grmhd/ms.pd
RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code
We have developed a new computer code, RAM, to solve the conservative
equations of special relativistic hydrodynamics (SRHD) using adaptive mesh
refinement (AMR) on parallel computers. We have implemented a
characteristic-wise, finite difference, weighted essentially non-oscillatory
(WENO) scheme using the full characteristic decomposition of the SRHD equations
to achieve fifth-order accuracy in space. For time integration we use the
method of lines with a third-order total variation diminishing (TVD)
Runge-Kutta scheme. We have also implemented fourth and fifth order Runge-Kutta
time integration schemes for comparison. The implementation of AMR and
parallelization is based on the FLASH code. RAM is modular and includes the
capability to easily swap hydrodynamics solvers, reconstruction methods and
physics modules. In addition to WENO we have implemented a finite volume module
with the piecewise parabolic method (PPM) for reconstruction and the modified
Marquina approximate Riemann solver to work with TVD Runge-Kutta time
integration. We examine the difficulty of accurately simulating shear flows in
numerical relativistic hydrodynamics codes. We show that under-resolved
simulations of simple test problems with transverse velocity components produce
incorrect results and demonstrate the ability of RAM to correctly solve these
problems. RAM has been tested in one, two and three dimensions and in
Cartesian, cylindrical and spherical coordinates. We have demonstrated
fifth-order accuracy for WENO in one and two dimensions and performed detailed
comparison with other schemes for which we show significantly lower convergence
rates. Extensive testing is presented demonstrating the ability of RAM to
address challenging open questions in relativistic astrophysics.Comment: ApJS in press, 21 pages including 18 figures (6 color figures
Collimated Jet or Expanding Outflow: Possible Origins of GRBs and X-Ray Flashes
We investigate the dynamics of an injected outflow propagating in a
progenitor in the context of the collapsar model for gamma-ray bursts (GRBs)
through two dimensional axisymmetric relativistic hydrodynamic simulations.
Initially, we locally inject an outflow near the center of a progenitor. We
calculate 25 models, in total, by fixing its total input energy to be 10^{51}
ergs s^{-1} and radius of the injected outflow to be cm while
varying its bulk Lorentz factor, , and its specific
internal energy, . The injected outflow propagates
in the progenitor and drives a large-scale outflow or jet. We find a smooth but
dramatic transition from a collimated jet to an expanding outflow among
calculated models. The maximum Lorentz factor is, on the other hand, sensitive
to both of and ; roughly . Our finding will explain a smooth transition between the
GRBs, X-ray rich GRBs (XRRs) and X-ray Flashes (XRFs) by the same model but
with different values.Comment: Comments 51 pages, 21 figures. accepted for publication in ApJ high
resolution version is available at
http://www.mpa-garching.mpg.de/~mizuta/COLLAPSAR/collapsar.htm
Type II critical phenomena of neutron star collapse
We investigate spherically-symmetric, general relativistic systems of
collapsing perfect fluid distributions. We consider neutron star models that
are driven to collapse by the addition of an initially "in-going" velocity
profile to the nominally static star solution. The neutron star models we use
are Tolman-Oppenheimer-Volkoff solutions with an initially isentropic,
gamma-law equation of state. The initial values of 1) the amplitude of the
velocity profile, and 2) the central density of the star, span a parameter
space, and we focus only on that region that gives rise to Type II critical
behavior, wherein black holes of arbitrarily small mass can be formed. In
contrast to previously published work, we find that--for a specific value of
the adiabatic index (Gamma = 2)--the observed Type II critical solution has
approximately the same scaling exponent as that calculated for an
ultrarelativistic fluid of the same index. Further, we find that the critical
solution computed using the ideal-gas equations of state asymptotes to the
ultrarelativistic critical solution.Comment: 24 pages, 22 figures, RevTeX 4, submitted to Phys. Rev.
Relativistic Hydrodynamics around Black Holes and Horizon Adapted Coordinate Systems
Despite the fact that the Schwarzschild and Kerr solutions for the Einstein
equations, when written in standard Schwarzschild and Boyer-Lindquist
coordinates, present coordinate singularities, all numerical studies of
accretion flows onto collapsed objects have been widely using them over the
years. This approach introduces conceptual and practical complications in
places where a smooth solution should be guaranteed, i.e., at the gravitational
radius. In the present paper, we propose an alternative way of solving the
general relativistic hydrodynamic equations in background (fixed) black hole
spacetimes. We identify classes of coordinates in which the (possibly rotating)
black hole metric is free of coordinate singularities at the horizon,
independent of time, and admits a spacelike decomposition. In the spherically
symmetric, non-rotating case, we re-derive exact solutions for dust and perfect
fluid accretion in Eddington-Finkelstein coordinates, and compare with
numerical hydrodynamic integrations. We perform representative axisymmetric
computations. These demonstrations suggest that the use of those coordinate
systems carries significant improvements over the standard approach, especially
for higher dimensional studies.Comment: 10 pages, 4 postscript figures, accepted for publication in Phys.
Rev.
- âŠ