Godunov type schemes, based on exact or approximate solutions to the R
iemann problem, have proven to be an excellent tool to compute approxi
mate solutions to hyperbolic systems of conservation laws. However, th
ere are many instances in which a particular scheme produces inappropr
iate results. In this paper we consider several situations in which Ro
e's scheme gives incorrect results (or blows up all together) and we p
ropose an alternative flux formula that produces numerical approximati
ons in which the pathological behavior is either eliminated or reduced
to computationally acceptable levels. (C) 1996 Academic Press, Inc.