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A numerical model for multiphase liquid-vapor-gas flows with interfaces and cavitation

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M. Pelanti (ENSTA ParisTech)

We are interested in the simulation of multiphase flows involving the liquid and vapor
phases of one species and a third inert gaseous phase. We describe these flows by a
hyperbolic single-velocity multiphase compressible 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 flow equations are solved by a
mixture-energy-consistent finite volume wave propagation scheme, combined with simple and robust
procedures for the treatment of the stiff relaxation terms. An analytical study of the characteristic
wave speeds of the hierarchy of relaxed models associated to the parent model system is also presented.
We show several numerical experiments, including two-dimensional simulations of underwater explosive
phenomena where highly pressurized gases trigger cavitation processes close to a rigid surface or to
a free surface.