Special-relativistic Smoothed Particle Hydrodynamics: a benchmark suite

TL;DR

This paper evaluates a new special-relativistic Smoothed Particle Hydrodynamics scheme through various challenging tests, demonstrating high accuracy in advection and shock problems, advancing computational methods for relativistic fluids.

Contribution

Introduces a novel special-relativistic SPH formulation with improved symmetry, artificial viscosity, and grad-h-terms, benchmarked against demanding test problems.

Findings

Performs near-perfect in pure advection tests

Produces accurate results in highly relativistic shock problems

Demonstrates robustness of the new scheme in relativistic fluid simulations

Abstract

In this paper we test a special-relativistic formulation of Smoothed Particle Hydrodynamics (SPH) that has been derived from the Lagrangian of an ideal fluid. Apart from its symmetry in the particle indices, the new formulation differs from earlier approaches in its artificial viscosity and in the use of special-relativistic ``grad-h-terms''. In this paper we benchmark the scheme in a number of demanding test problems. Maybe not too surprising for such a Lagrangian scheme, it performs close to perfectly in pure advection tests. What is more, the method produces accurate results even in highly relativistic shock problems.