Abstract
ABSTRACT We present an update on the General-relativistic multigrid numerical (Gmunu) code, a parallelized, multidimensional curvilinear, general relativistic magnetohydrodynamics code with an efficient non-linear cell-centred multigrid elliptic solver, which is fully coupled with an efficient block-based adaptive mesh refinement module. To date, as described in this paper, Gmunu is able to solve the elliptic metric equations in the conformally flat condition approximation with the multigrid approach and the equations of ideal general-relativistic magnetohydrodynamics by means of high-resolution shock-capturing finite-volume method with reference metric formularised multidimensionally in Cartesian, cylindrical, or spherical geometries. To guarantee the absence of magnetic monopoles during the evolution, we have developed an elliptical divergence cleaning method by using the multigrid solver. In this paper, we present the methodology, full evolution equations and implementation details of Gmunu and its properties and performance in some benchmarking and challenging relativistic magnetohydrodynamics problems.
Highlights
Many astrophysical scenarios involving neutron stars and black holes such as core-collapse supernovae, mergers of compact objects are the most important events in gravitational wave physics or multimessenger astrophysics
We present an update on the General-relativistic multigrid numerical (Gmunu) code, a parallelised, multi-dimensional curvilinear, general relativistic magnetohydrodynamics code with an efficient non-linear cell-centred multigrid elliptic solver, which is fully coupled with an efficient block-based adaptive mesh refinement module
In our previous work Cheong et al (2020), we presented an axisymmetric general relativistic hydordynamics code Gmunu (General-relativistic multigrid numerical solver) and show that cell-centred multigrid method is an efficient and robust approach of solving the elliptic metric equations in the conformally flat condition (CFC) approximation Dimmelmeier et al (2002); Cordero-Carrión et al (2009)
Summary
Many astrophysical scenarios involving neutron stars and black holes such as core-collapse supernovae, mergers of compact objects are the most important events in gravitational wave physics or multimessenger astrophysics. Depending on the configuration and focus of the problems, the computational cost can be significantly reduced if some symmetries can be imposed or simulating the problems in certain geometries, e.g. core-collapse supernovae Janka et al (2007); Burrows (2013), mangetars Turolla et al (2015); Mereghetti et al (2015); Kaspi & Beloborodov (2017), pulsars Lorimer (2005), compact binary merger remnants Shibata & Taniguchi (2011); Faber & Rasio (2012); Baiotti & Rezzolla (2017); Duez & Zlochower (2019); Radice et al (2020), and self-gravitating accretion disks Abramowicz & Fragile (2013) While these problems can be simulated in three-dimensional Cartesian coordinate, these systems with approximate symmetries are better captured in spherical or cylindrical coordinates due to better angular momentum conservation. Greek indices, running from 0 to 3, are used for 4-quantities while the Roman indices, running from 1 to 3, are used for 3-quantities
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