Validation of hyperbolic model for two-phase flow in conservative form

A mathematical formulation is proposed for the solution of equations governing isentropic gas-liquid flow. The model considered here is a two-fluid model type where the relative velocity between the two phases is implemented by a kinetic constitutive equation. Starting from the conservation of mass and momentum laws, a system of three differential equations is derived in a conservative form for the three principal variables, which are mixture density, mixture velocity and the relative velocity. The governing equations for the mixture offer the novel hyperbolic conservation laws for the description of two-phase flows without any conventional source terms in the momentum or relative velocity equations. The discretisation of the governing equations is based on splitting approach, which is specially designed to allow a straightforward extension to various numerical methods such as Godunov methods of centred-type. To verify the validity of the model, numerical results are presented and discussed. It is demonstrated that the proposed numerical methods have superior overall numerical accuracy among existing methods and models in the literature. The model correctly describes the formation of shocks and rarefactions for the solution of discontinuities in two-phase fluid flow problems, thus verifying the proposed mathematical and numerical investigations.