  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 pre-processing,
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 cancells and factorizes a number of terms helping to
amortiguate 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.
