Zanna, L.: Primitive variable solvers for conservative general relativistic magnetohydrodynamics

Conservative numerical schemes for general relativistic magnetohydrodynam-ics (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 in-verse transformation (conserved to primitive) requires the solution of a set of ve nonlinear equations. Here we discuss the mathematical properties of the inverse { 2 { transformation and present six numerical methods for performing the inversion. The rst method solves the full set of ve nonlinear equations directly using a Newton-Raphson scheme and a guess from the previous timestep. The other methods reduce the ve nonlinear equations to either one or two nonlinear equa-tions 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. Subject headings: hydrodynamics | methods: numerical | MH