Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics
Abstract
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.
Keywords
Cite
@article{arxiv.astro-ph/0512420,
title = {Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics},
author = {Scott C. Noble and Charles F. Gammie and Jonathan C. McKinney and Luca Del Zanna},
journal= {arXiv preprint arXiv:astro-ph/0512420},
year = {2009}
}
Comments
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.pdf