A numerical model for three-phase liquid–vapor–gas flows with relaxation processes

We are interested in three-phase flows involving the liquid and vapor phases of one species and a third inert gaseous phase. We describe these flows by a single-velocity multiphase flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical and thermal relaxation source terms for all the phases and chemical relaxation terms to describe mass transfer between the liquid and vapor phases of the species that may undergo transition. The homogeneous hyperbolic portion of the equations is solved numerically via a finite volume wave propagation scheme. Relaxation terms are treated by routines that exploit algebraic equilibrium conditions for the relaxed states. We present numerical results for a three-phase cavitation tube test, showing that the predicted wave speed for different levels of activation of instantaneous relaxation processes agrees with the theoretical findings on the sub-characteristic interlacing of the wave speeds of the corresponding hierarchy of relaxed models. A two-dimensional simulation of an underwater explosion is also presented.