CAPTURING SHOCK REFLECTIONS - AN IMPROVED FLUX FORMULA

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.