Gmunu: Paralleled, grid-adaptive, general-relativistic magnetohydrodynamics in curvilinear geometries in dynamical spacetimes

TL;DR

Gmunu is a parallelized, multi-dimensional general relativistic magnetohydrodynamics code with adaptive mesh refinement and an elliptic solver, enabling efficient simulations of complex astrophysical phenomena in curvilinear geometries.

Contribution

This paper introduces Gmunu, a novel code integrating multigrid elliptic solvers with adaptive mesh refinement for general relativistic MHD in curvilinear coordinates.

Findings

Successfully solves elliptic metric equations in CFC approximation

Maintains magnetic divergence-free condition with elliptical divergence cleaning

Demonstrates high performance in relativistic MHD benchmarks

Abstract

We present an update of the General-relativistic multigrid numerical (Gmunu) code, a parallelized, multi-dimensional curvilinear, general relativistic magnetohydrodynamics code with an efficient non-linear cell-centred multigrid (CCMG) elliptic solver, which is fully coupled with an efficient block-based adaptive mesh refinement modules. Currently, Gmunu is able to solve the elliptic metric equations in the conformally flat condition (CFC) 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 formularise multi-dimensionally 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 multigrid solver. In this paper, we present the methodology, full evolution equations and implementation details of our code Gmunu and its properties and performance in some benchmarking and challenging relativistic magnetohydrodynamics problems.