An extension of Gmunu: General-relativistic resistive magnetohydrodynamics based on staggered-meshed constrained transport with elliptic cleaning

TL;DR

This paper extends the Gmunu code to include general-relativistic resistive magnetohydrodynamics with advanced divergence-free magnetic field handling, enabling robust simulations of magnetized neutron stars across various resistivity regimes.

Contribution

It introduces a new implementation of resistive MHD in Gmunu with three divergence-free methods, including a novel elliptic cleaning approach applicable to staggered grids.

Findings

The code accurately recovers a wide range of resistivity in tests.

Elliptic cleaning improves divergence-free magnetic field preservation.

Applications demonstrate realistic modeling of magnetized neutron stars.

Abstract

We present the implementation of general-relativistic resistive magnetohydrodynamics solvers and three divergence-free handling approaches adopted in the General-relativistic multigrid numerical (Gmunu) code. In particular, implicit-explicit Runge-Kutta schemes are used to deal with the stiff terms in the evolution equations for small resistivity. Three divergence-free handling methods are (i) hyperbolic divergence cleaning through a generalised Lagrange multiplier (GLM); (ii) staggered-meshed constrained transport (CT) schemes and (iii) elliptic cleaning though multigrid (MG) solver which is applicable in both cell-centred and face-centred (stagger grid) magnetic field. The implementation has been test with a number of numerical benchmarks from special-relativistic to general-relativistic cases. We demonstrate that our code can robustly recover a very wide range of resistivity. We also illustrate the applications in modelling magnetised neutron stars, and compare how different divergence-free handling affects the evolution of the stars. Furthermore, we show that the preservation of the divergence-free condition of magnetic field when staggered-meshed constrained transport schemes can be significantly improved by applying elliptic cleaning.