Gmunu: paralleled, grid-adaptive, general-relativistic magnetohydrodynamics in curvilinear geometries in dynamical space–times

Abstract

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. 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 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 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.

An Extension of Gmunu: General-relativistic Resistive Magnetohydrodynamics Based on Staggered-meshed Constrained Transport with Elliptic Cleaning

“…As in Cheong et al (2021), under the reference-metric formalism, the evolution equations can be expressed as…”

“…If the electric field E i and the magnetic field B i are given, the conserved variables q can then be transformed into primitive variables (ρ, Wv i , p) using the method for general-relativistic hydrodynamics described in Cheong et al (2020Cheong et al ( , 2021 by removing the electromagnetic part.…”

“…In previous work (Cheong et al 2021), we presented the first general-relativistic MHD code in the literature to adopt elliptic divergence cleaning as the divergence-free treatment during the evolution. This scheme was developed only for the magnetic field defined at cell centers.…”

“…For the simulations of neutron stars, we used the same refinement setting as in our previous work (Cheong et al 2021). In particular, we defined a relativistic gravitational potential Φ := 1 − α.…”

“…In this work, we extend Gmunu by implementing the IMEXbased general-relativistic resistive MHD framework. In addition to elliptical divergence cleaning for magnetic field, which removes the magnetic monopoles by solving Poisson's equation, as established in our previous work (Cheong et al 2021), we included two more approaches to handle the solenoidal condition, namely, (i) hyperbolic divergence cleaning through a generalized Lagrange multiplier (GLM) (see a Newtonian example in Dedner et al 2002), and (ii) a constrained transport (CT) scheme that updates the magnetic fields while controlling the divergence-free constraint to numerical round-off accuracy (Evans & Hawley 1988). Finally, our code is validated through some benchmarking tests.…”