Simulating magnetized neutron stars with discontinuous Galerkin methods

TL;DR

This paper evaluates various limiting strategies for discontinuous Galerkin methods in simulating magnetized neutron stars, finding that a hybrid DG-finite difference approach is most robust without parameter tuning.

Contribution

It provides a comprehensive comparison of limiting strategies in DG methods for relativistic magnetohydrodynamics, identifying the hybrid DG-FD method as the most effective.

Findings

Hybrid DG-FD method is most robust for simulations.

Most limiters require fine-tuning for stability.

Discontinuous Galerkin methods are effective for complex astrophysical simulations.

Abstract

Discontinuous Galerkin methods are popular because they can achieve high order where the solution is smooth, because they can capture shocks while needing only nearest-neighbor communication, and because they are relatively easy to formulate on complex meshes. We perform a detailed comparison of various limiting strategies presented in the literature applied to the equations of general relativistic magnetohydrodynamics. We compare the standard minmod/$\Lambda\Pi^N$ limiter, the hierarchical limiter of Krivodonova, the simple WENO limiter, the HWENO limiter, and a discontinuous Galerkin-finite-difference hybrid method. The ultimate goal is to understand what limiting strategies are able to robustly simulate magnetized TOV stars without any fine-tuning of parameters. Among the limiters explored here, the only limiting strategy we can endorse is a discontinuous Galerkin-finite-difference hybrid method.