An efficient implementation of flux formulae in multidimensional relativistic hydrodynamical codes

We derive and analyze a simplified formulation of the numerical viscosity t erms appearing in the expression of the numerical fluxes associated to seve ral High-Resolution Shock-Capturing schemes. After some algebraic preproces sing, we give explicit expressions for the numerical viscosity terms of two of the most widely used flux formulae, which implementation saves computat ional time in multidimensional simulations of relativistic flows. Additiona lly, such treatment explicitely cancels and factorizes a number of terms he lping to damp the growing of round-off errors. We have checked the performa nce of our formulation running a 3D relativistic hydrodynamical code to sol ve a standard test-bed problem and found that the improvement in efficiency is of high practical interest in numerical simulations of relativistic flo ws in Astrophysics. (C) 1999 Elsevier Science B.V. All rights reserved.