A mixture-energy-consistent numerical approximation of a two-phase flow model for fluids with interfaces and cavitation

We model cavitating flows by a variant of the six-equation singlevelocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas– Berry [J. Comput. Phys. 228, 1678 (2009)]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure with the correct mixture equation of state. The two-phase system is solved in two dimensions by a fully-discretized high-resolution wave propagation scheme based on a HLLC/Roe Riemann solver. Numerical experiments show the ability of the numerical model to describe mechanical cavitation processes.