A class of approximate Riemann solvers and their relation to relaxation schemes

We show that a simple relaxation scheme of the type proposed by Jin and Xin [Comm. Pure Appl. Math. 48, 235 (1995)] can be reinterpreted as defining a particular approximate Riemann solver for the original system of m conserv ation laws. Based on this observation, a more general class of approximate Riemann solvers is proposed which allows as many as 2m waves in the resulti ng solution. These solvers are related to more general relaxation systems a nd connections with several other standard solvers are explored. The added flexibility of 2m waves may be advantageous in deriving new methods. Some p otential applications are explored for problems with discontinuous flux fun ctions or source terms. (C) 2001 Academic Press.