Implementing a new recovery scheme for primitive variables in the general relativistic magnetohydrodynamic code Spritz

Abstract

General relativistic magnetohydrodynamic (GRMHD) simulations represent a fundamental tool to probe various underlying mechanisms at play during binary neutron star (BNS) and neutron star (NS) - black hole (BH) mergers. Contemporary flux-conservative GRMHD codes numerically evolve a set of conservative equations based on `conserved' variables which then need to be converted back into the fundamental (`primitive') variables. The corresponding conservative-to-primitive variable recovery procedure, based on root-finding algorithms, constitutes one of the core elements of such GRMHD codes. Recently, a new robust, accurate and efficient recovery scheme called RePrimAnd was introduced, which has demonstrated the ability to always converge to a unique solution. The scheme provides fine-grained error policies to handle invalid states caused by evolution errors, and also provides analytical bounds for the error of all primitive variables. In this work, we describe the technical aspects of implementing the RePrimAnd scheme into the GRMHD code Spritz. To check our implementation as well as to assess the various features of the scheme, we perform a number of GRMHD tests in three dimensions. Our tests, which include critical cases such as a NS collapse to a BH as well as the early evolution (~50 ms) of a Fishbone-Moncrief BH-accrection disk system, show that RePrimAnd is able to support magnetized, low density environments with magnetic-to-fluid pressure ratios as high as 10^4, in situations where the previously used recovery scheme fails.