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.