Simplified discretization of systems of hyperbolic conservation laws containing advection equations

The high speed flow of complex materials can often be modeled by the compre ssible Euler equations coupled to (possibly many) additional advection equa tions. Traditionally, good computational results have been obtained by writ ing these systems in fully conservative form and applying the general metho dology of shock-capturing schemes for systems of hyperbolic conservation la ws. In this paper, we show how to obtain the benefits of these schemes with out the usual complexity of full characteristic decomposition or the restri ctions imposed by fully conservative differencing. Instead, under certain c onditions defined in Section 2, the additional advection equations can be d iscretized individually with a nonconservative scheme while the remaining s ystem is discretized using a fully conservative approach, perhaps based on a characteristic field decomposition. A simple extension of the Lax-Wendrof f Theorem is presented to show that under certain verifiable hypothesis, ou r nonconservative schemes converge to weak solutions of the fully conservat ive system. Then this new technique is applied to systems of equations from compressible multiphase flow, chemically reacting flow, and explosive mate rials modeling. In the last instance, the flexibility introduced by this ap proach is exploited to change a weakly hyperbolic system into an equivalent strictly hyperbolic system, and to remove certain nonphysical modeling ass umptions. (C) 2000 Academic Press.