Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics Export

@misc{citeulike:620609, 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.}, archivePrefix = {arXiv}, author = {Noble, Scott C. and Gammie, Charles F. and Mckinney, Jonathan C. and Del Zanna, Luca}, citeulike-article-id = {620609}, citeulike-linkout-0 = {http://arxiv.org/abs/astro-ph/0512420}, citeulike-linkout-1 = {http://arxiv.org/pdf/astro-ph/0512420}, day = {15}, eprint = {astro-ph/0512420}, keywords = {gr, grmhd, mhd, simulation}, month = {Dec}, posted-at = {2006-05-09 18:45:37}, priority = {2}, title = {Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics}, url = {http://arxiv.org/abs/astro-ph/0512420}, year = {2005} }

TY - ELEC ID - citeulike:620609 L3 - citeulike-article-id:620609 N2 - 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. TI - Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics KW - gr KW - grmhd KW - mhd KW - simulation AU - Noble, Scott AU - Gammie, Charles AU - Mckinney, Jonathan AU - Del Zanna, Luca PY - 2005/Dec/15/ UR - http://arxiv.org/abs/astro-ph/0512420 ER -