Numerical investigation of a mixture two-phase flow model in two-dimensional space

•A two-dimensional two-phase flow with velocity non-equilibrium is presented.•Numerical simulations are based on a fully hyperbolic and conservative mixture model that include a relative velocity equation.•Finite volume Godunov methods are extended to the mixture model.•Validation and comparison of a mixture model gas-liquid flows. A two-dimensional two-phase flow model for gas-liquid mixture is presented. The model takes into account the relative velocity between the gas and liquid phases and is based on conservation equations for gas-liquid mixtures. The mixture model involves balance equations for the relative velocity and is able to handle it without any physical or artificial stabilization in the source terms. The novel aspect of the mixture model is that it is written in a conservative form and ensures the hyperbolicity of the two-phase flow equations. With this regard, the governing equations are solved with finite volume methods. We extend and apply the framework of Godunov methods of centred-type, namely, the FirstOrder Centered (FORCE) and the Slope Limiter Centered (SLIC) methods to the two-dimensional governing equations without any loss of generality in the numerical solutions. An efficient assessment of both the mixture model and the numerical methods is carried out by simulating physical problems available in the literature. Simulations agree well with those in the literature and include new insights that could be used to explain the relative velocity observations. The favourable results suggest that the two-dimensional mixture model simulations can be employed for practical engineering problems of the non-equilibrium type.