The effect of interfacial pressure in the discrete-equation multiphase model

Abstract

Abgrall and Saurel [Abgrall R, Saurel R. Discrete equations for physical and numerical compressible multiphase mixtures. J Comput Phys 2003;186(2):361–396] presented a discrete-equation two-pressure two-phase model of seven equations. A main characteristic of that model is that the Riemann problems are solved between two pure fluids, and that phase interaction is determined by the Riemann solver. Here we propose a five-equation isentropic simplification of the discrete-equation model, and by examples we show how existing and new models for interfacial closures can be incorporated into it. The interfacial pressure has a determining effect on the final solution. We further show that the discrete-equation model can reproduce results for two-phase shock tubes given in the literature when the adequate interfacial-pressure model is employed. Finally, we compare the present results with those of a continuous five-equation model, and obtain very good agreement.