A three-phase flow model

We present here a three-fluid three-pressure model to describe three-field patterns or three-phase flows. The basic ideas rely on the counterpart of the two-fluid two-pressure model which has been introduced in the DDT (deflagration to detonation theory) framework, and has been more recently extended to liquid–vapour simulations. We first show that the system is hyperbolic without any constraining condition on the flow patterns. This is followed by a detailed investigation of the structure of single waves in the Riemann problem. Smooth solutions of the whole system are shown to be in agreement with physical requirements on void fractions, densities, and specific entropies. A simple fractional step method, which handles separately convective patterns and source terms, is used to compute approximations of solutions. A few computational results illustrate the whole approach.