Relativistic MHD and black hole excision: Formulation and initial tests

TL;DR

This paper introduces a novel algorithm for solving relativistic MHD equations with black hole excision, employing overlapping grids and divergence cleaning techniques, validated through standard tests in flat space.

Contribution

It presents a new scheme integrating black hole excision with smooth boundaries into relativistic MHD simulations, utilizing AMR and divergence cleaning methods.

Findings

Successful implementation of excision with overlapping grids

Comparison of elliptic and hyperbolic divergence cleaning techniques

Validation through standard test problems in flat space

Abstract

A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids, and elliptic and hyperbolic divergence cleaning.