Abstract: This paper describes a new approach to the numerical simulation of a one-dimensional isentropic mixture of liquid and vapour without phase change. It amounts to two conservation laws for the mixture coupled by a relative velocity conservation equation. Under certain restrictions the resulting system of conservation law is hyperbolic and allows discontinuous solution. We present high-resolution TVD schemes with an approximate Riemann solver for the resolution of conservation equations. To illustrate the capabilities of the proposed methods, results are presented for carefully chosen test problems. The results show that our numerical schemes are more accurate than other schemes currently used.
Conservation Laws Preprint Server <email@example.com> 2003-04-24 08:03:32 UTC