A high-order shock capturing discontinuous Galerkin-finite-difference hybrid method for GRMHD

TL;DR

This paper introduces a hybrid numerical scheme combining discontinuous Galerkin and finite-difference methods for high-order, shock-capturing simulations in general relativistic magnetohydrodynamics, suitable for complex astrophysical phenomena.

Contribution

A novel hybrid scheme that adaptively switches between discontinuous Galerkin and finite-difference methods for improved shock capturing in GRMHD simulations.

Findings

Effective handling of shocks and discontinuities in 1D, 2D, and 3D tests.

High-order accuracy and exponential convergence in smooth regions.

Robust simulation of neutron star mergers.

Abstract

We present a discontinuous Galerkin-finite-difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited discontinuous Galerkin candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust finite-difference methods. Because of its a posteriori nature, the hybrid scheme inherits the best properties of both methods. It is high-order with exponential convergence in smooth regions, while robustly handling discontinuities. We give a detailed description of how we transfer the solution between the discontinuous Galerkin and finite-difference solvers, and the troubled-cell indicators necessary to robustly handle slow-moving discontinuities and simulate magnetized neutron stars. We demonstrate the efficacy of the proposed method using a suite of standard and very challenging 1d, 2d, and 3d relativistic magnetohydrodynamics test problems. The hybrid scheme is designed from the ground up to efficiently simulate astrophysical problems such as the inspiral, coalescence, and merger of two neutron stars.