A high resolution numerical scheme for a high speed gas-liquid two-phase flow

A high resolution numerical method for solving high speed gas-liquid two-phase flow is proposed and applied to the two-phase shock tube problem. The present method employs a finite-difference 4th-order Runge-Kutta method and Roe’s flux difference splitting approximation with the MUSCL TVD scheme. A homogeneous equilibrium gas-liquid two-phase model that takes account of the compressibility of mixed media is used. Therefore, the present density-based numerical method permits simple treatment of the whole gasliquid two-phase flow field, including wave propagation, large density changes and incompressible flow characteristics at the low Mach number. The speed of sound of above two-phase media has been derived on the basis of thermodynamic relations. By this method, a Riemann problem for the Euler equations of a one-dimensional shock tube was computed. Numerical results such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media at thermal and isothermal conditions, and some features related to computational efficiency are made. Comparisons of predicted results with exact solutions are provided and discussed.