An efficient implementation of flux formulae in multidimensional relativistic hydrodynamical codes

Abstract

We derive and analyze a simplified formulation of the numerical viscosity terms appearing in the expression of the numerical fluxes associated to several High-Resolution Shock-Capturing schemes. After some algebraic preprocessing, we give explicit expressions for the numerical viscosity terms of two of the most widely used flux formulae, which implementation saves computational time in multidimensional simulations of relativistic flows. Additionally, such treatment explicitely cancels and factorizes a number of terms helping to damp the growing of round-off errors. We have checked the performance of our formulation running a 3D relativistic hydrodynamical code to solve a standard test-bed problem and found that the improvement in efficiency is of high practical interest in numerical simulations of relativistic flows in Astrophysics.