An entropy consistent and symmetric seven-equation model for compressible two-phase flows

Abstract

We propose new seven-equation model and related solution methods for compressible two-phase flows. The model is built on new closure laws for the interaction between the coexisting two phases. It takes a symmetric form for the two phases and shares some favorable properties with the well-known Baer-Nunziato model [4]: the equations system is unconditionally hyperbolic and is conservative for the total momentum and energy; the interfacial interaction between phases is an isentropic process for each phase. Moreover, it permits to obtain a linear degenerate field associated with the wave which separates the mixture, and the full set of the associated Riemann invariants can be derived explicitly. The pressure and velocity relaxation terms are included for the additional interaction between phases. Numerical approximation of the entire model is performed in an operator splitting manner – two Godunov-type schemes utilizing respectively a HLL solver and a composite approximate Riemann solver are used to discretize the homogeneous system; stable implicit algorithms are explored for the non-instantaneous pressure and velocity relaxations. Several examples are provided to illustrate the property of the new model and the capability of the solution methods.