A Discontinuous Galerkin Method for General Relativistic Hydrodynamics in thornado

TL;DR

This paper develops a high-order Discontinuous Galerkin method for solving general relativistic hydrodynamics equations, demonstrating its accuracy and robustness through complex test problems relevant to astrophysics.

Contribution

It introduces a DG solver for 3+1 general relativistic hydrodynamics with conformally-flat approximation, validated by challenging test cases.

Findings

Accurate solutions for relativistic Kelvin--Helmholtz instability

Robust handling of relativistic Riemann problems

Encouraging results on standing accretion shock instability

Abstract

Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while, with the aid of limiters, still resolving strong shocks. These and other properties make DG methods attractive for solving problems involving hydrodynamics; e.g., the core-collapse supernova problem. With that in mind we are developing a DG solver for the general relativistic, ideal hydrodynamics equations under a 3+1 decomposition of spacetime, assuming a conformally-flat approximation to general relativity. With the aid of limiters we verify the accuracy and robustness of our code with several difficult test-problems: a special relativistic Kelvin--Helmholtz instability problem, a two-dimensional special relativistic Riemann problem, and a one- and two-dimensional general relativistic standing accretion shock (SAS) problem. We find good agreement with published results, where available. We also establish sufficient resolution for the 1D SAS problem and find encouraging results regarding the standing accretion shock instability (SASI) in 2D.