Capturing shock reflections: An improved flux formula

Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In this paper we consider several situations in which Roe's scheme gives incorrect results (or blows up all together) and we propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels. (C) 1996 Academic Press, Inc.