Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows

Homogeneous equilibrium two-phase flows are characterized by important variations of the local Mach number. Indeed, the sound speed can be several orders of magnitude higher in the liquid phase than in the two-phase mixture. For the simulation of such flows, a numerical method which can handle accurately any Mach number is thus necessary. In this paper, we investigate the applicability of preconditioned finite volume schemes for these problems. Specifically, we use Roeʹs scheme with Turkelʹs preconditioning, in a time-consistent formulation which allows transient computations. We introduce an original extension of Roeʹs scheme to fluids with arbitrary equations of state. We establish some stability results for the method. Numerical results are given for a two-phase bump channel flow in subsonic and transonic regimes.