A Time Consistent Method by Preconditioning of the Diffusion Term for Unsteady Gas-Liquid Two-Phase Flows

. A time accurate and high resolution numerical method for gas-liquid two-phase flows is proposed. The artificial viscous terms in the flux splitting of upwinding are derived by using the preconditioner to enhance the stability of computation for compressible and incompressible combined flow with arbitrary void fractions. A homogeneous equilibrium gas-liquid two-phase model taken account of the compressibility of mixed media is used. A finite-difference 4th-order Runge-Kutta method and a Roe-type flux splitting method with the MUSCL TVD scheme are employed. By this method, a one-dimensional two-phase shock tube problem was computed and confirmed the applicability to the unsteady and arbitrary Mach number flow problems. Detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and comparisons of predicted results with exact solutions are made.