A Pressure-Based Model for Two-Phase Flows Under Generic Equations of State

We present a diffuse interface method for a pressure-based Baer-Nunziato type model for compressible two-phase flows, which allows the use of generic equations of state to describe each phase. The model is made dimensionless by means of a special pressure scaling that recovers the correct scaling of the discrete governing equations in the zero Mach limit, and overcomes the difficulties related to the lack of a clear notion of reference speed of sound in non-equilibrium two-phase flows. The model is equipped with pressure and velocity relaxation terms to impose the mechanical equilibrium between phases after their independent evolution. Two different finite volume schemes are presented. First, a 1D semi-implicit staggered scheme is introduced to show the capability of the model to work with the Peng-Robinson EOS when each phase evolves close to the saturation curve. Then, a preliminary 2D explicit scheme, which does not include the relaxation terms, is presented as a first step toward the development of an unstructured 2D scheme for compressible two-phase flows at all Mach numbers. The validity of the preliminary 2D monolithic implementation of the hyperbolic operator is illustrated through the simulation of a shock-bubble interaction with air and helium.