Comparing the first and second order theories of relativistic dissipative fluid dynamics using the 1+1 dimensional relativistic flux corrected transport algorithm

TL;DR

This paper compares first and second order relativistic dissipative fluid theories using a flux corrected transport algorithm, showing that Israel-Stewart theory offers more stable and smoother numerical results than Navier-Stokes.

Contribution

It provides a numerical comparison of relativistic fluid theories in 1+1 dimensions, highlighting the stability and accuracy advantages of Israel-Stewart over Navier-Stokes.

Findings

Israel-Stewart theory yields more stable numerical solutions.

Results are smoother with Israel-Stewart equations.

Comparison performed using flux corrected transport algorithm.

Abstract

Focusing on the numerical aspects and accuracy we study a class of bulk viscosity driven expansion scenarios using the relativistic Navier-Stokes and truncated Israel-Stewart form of the equations of relativistic dissipative fluids in 1+1 dimensions. The numerical calculations of conservation and transport equations are performed using the numerical framework of flux corrected transport. We show that the results of the Israel-Stewart causal fluid dynamics are numerically much more stable and smoother than the results of the standard relativistic Navier-Stokes equations.