A time consistent preconditioning method for unsteady gas-liquid two-phase flows.

A time consistent preconditioning method for gas-liquid two-phase flows is proposed and applied to the two-phase shock tube problem. A finite-difference 4th-order Runge-Kutta method and a Roe-type flux splitting method with the MUSCL TYD scheme are employed. The artificial viscous terms in the flux splitting are modified by using the preconditioner to enhance the stability of computation for compressible and incompressible flow with arbitrary Mach numbers. A homogeneous equilibrium gas-liquid two-phase model taken account of the compressibility of mixed media is used. Therefore, the present method permits simple treatment of the whole gas-liquid two-phase flow field including wave propagation, large density changes and incompressible flow characteristics at the low Mach number. By this method, a Riemann problem for the one-dimensional Euler equations 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 provided and discussed. [ABSTRACT FROM AUTHOR]