A new shock-capturing numerical scheme for ideal hydrodynamics

TL;DR

This paper introduces a novel shock-capturing numerical scheme for ideal relativistic hydrodynamics that achieves high accuracy and low numerical viscosity by utilizing an exact Riemann solver within a Godunov framework.

Contribution

It presents a new algorithm that combines Godunov's method with an exact Riemann solver for arbitrary equations of state, improving precision in relativistic hydrodynamics simulations.

Findings

Achieves low numerical viscosity and high precision.

Successfully passes standard tests like sound wave propagation and shock tube.

Applicable to arbitrary equations of state.

Abstract

We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.