A Robust, Performance-Portable Discontinuous Galerkin Method for Relativistic Hydrodynamics

TL;DR

This paper introduces a robust, performance-portable discontinuous Galerkin method for relativistic hydrodynamics, incorporating novel variable recovery and state enforcement techniques, and demonstrates its effectiveness and efficiency on CPU and GPU architectures.

Contribution

The paper presents a new discontinuous Galerkin method with innovative primitive variable recovery and state enforcement, implemented using Kokkos for performance portability across CPUs and GPUs.

Findings

Effective simulation of relativistic Kelvin-Helmholtz instability.

Achieved high performance on both CPUs and GPUs.

Enhanced robustness in maintaining physically valid states.

Abstract

In this work, we present a discontinuous-Galerkin method for evolving relativistic hydrodynamics. We include an exploration of analytical and iterative methods to recover the primitive variables from the conserved variables for the ideal equation of state and the Taub-Matthews approximation to the Synge equation of state. We also present a new operator for enforcing a physically permissible conserved state at all basis points within an element while preserving the volume average of the conserved state. We implement this method using the Kokkos performance-portability library to enable running at performance on both CPUs and GPUs. We use this method to explore the relativistic Kelvin- Helmholtz instability compared to a finite volume method. Last, we explore the performance of our implementation on CPUs and GPUs.