Numerical modelling of compressible two-phase flows

This paper presents a hierarchy of compressible two-phase flow models. It is shown that using Chapman-Enskog expansions in the limit of zero relaxation time toward the various equilibria that exist in these flows, a full set of models of decreasing complexity can be constructed. At the top of this hierarchy, we have a complete seven equation model with two pressures, two velocities and two temperatures while the simplest model is given in the inviscid case by the Euler equations of compressible flows. We also show how some non-equilibrium effect can be retained in these models under the form of second-order dissipative terms. This paper concludes by some representative test-cases