Numerical tests of causal relativistic dissipative fluid dynamics

TL;DR

This paper develops and tests numerical methods for solving the Israel-Stewart equations of causal relativistic dissipative fluid dynamics, focusing on the Riemann problem in multiple dimensions, with applications to realistic 3+1D modeling.

Contribution

The paper introduces numerical schemes for Israel-Stewart equations and demonstrates their effectiveness through multidimensional Riemann problem tests.

Findings

Numerical methods successfully solve 1+1 and 2+1 dimensional Riemann problems.

Schemes are applicable to realistic 3+1 dimensional relativistic fluid simulations.

Results support the stability and accuracy of the proposed numerical approaches.

Abstract

We present numerical methods to solve the Israel-Stewart (IS) equations of causal relativistic dissipative fluid dynamics with bulk and shear viscosities. We then test these methods studying the Riemann problem in (1+1)-- and (2+1)-dimensional geometry. The numerical schemes investigated here are applicable to realistic (3+1)--dimensional modeling of a relativistic dissipative fluid.