Numerical approximation of a degenerated non-conservative multifluid model: relaxation scheme

The present work is devoted to the numerical approximation of a system which arises when modelling a two-phase flow in a pipeline. Two particular difficulties are of special interest, the non-conservativity and the weakly hyperbolicity of this system. Some elementary waves are characterized and a relaxation system, unconditionally hyperbolic, is proposed. The stability criteria of the resulting relaxation method are achieved by a Chapmann Enskog-like expansion. A numerical scheme based on the relaxation system is proposed and computations are performed on a shock tube. Validation is performed by comparison with the exact solution and also to the solution from a modified HLL scheme. Copyright (c) 2005 John Wiley & Sons, Ltd.