A FLUX-SPLIT ALGORITHM APPLIED TO RELATIVISTIC FLOWS

The equations of RFD can be written as a hyperbolic system of conserva tion laws by choosing an appropriate vector of unknowns, We give an ex plicit formulation of the full spectral decomposition of the Jacobian matrices associated with the fluxes in each spatial direction, which i s the essential ingredient of the techniques we propose in this paper. These techniques are based on the recently derived flux formula of Ma rquina, a new way to compute the numerical flux at a cell interface wh ich leads to a conservative, upwind numerical scheme. Using the spectr al decompositions in a fundamental way, we construct high order versio ns of the basic First-order scheme described by R. Donat and A. Marqui na in (J. Comput. Phys. 125, 42 (1996)) and test their performance in several standard simulations in one dimension. Two-dimensional simulat ions include a wind tunnel with a flat faced step and a supersonic jet stream, both of them in strongly ultrarelativistic regimes. (C) 1998 Academic Press.