SUMMARYThis paper is to continue our previous work Niu (Int. J. Numer. Meth. Fluids 2001; 36:351-371) on solving a two-fluid model for compressible liquid-gas flows using the AUSMDV scheme. We first propose a pressure-velocity-based diffusion term originally derived from AUSMDV scheme Wada and Liou (SIAM J. Sci. Comput. 1997; 18(3):633-657) to enhance its robustness. The scheme can be applied to gas and liquid fluids universally. We then employ the stratified flow model Chang and Liou (J. Comput. Physics 2007; 225:240-873) for spatial discretization. By defining the fluids in different regions and introducing inter-phasic force on cell boundary, the stratified flow model allows the conservation laws to be applied on each phase, and therefore, it is able to capture fluid discontinuities, such as the fluid interfaces and shock waves, accurately. Several benchmark tests are studied, including the Ransom's Faucet problem, 1D air-water shock tube problems, 2D shock-water column and 2D shock-bubble interaction problems. The results indicate that the incorporation of the new dissipation into AUSM + -up scheme and the stratified flow model is simple, accurate and robust enough for the compressible multi-phase flows.

In this work, a pressure-velocity coupling is proposed to modify the advection flux splitting for achieving accurate simulation of cavitated bubbly flows. As we know, the resolution of interface pressure waves among multiphase flows based on compressible Eulerian schemes is still a challenging topic. The current study evaluates the numerical diffusive terms in the AUSM-type scheme and suggests a robust implementation to deal with the pressure-velocity coupling term in AUSMþ . The proposed modification of AUSMþ is shown to enhance accurate resolution of phase interfaces and liquid pressure waves in unsteady cavitated shot tube problems and the calculations of external cavitated flows after comparing with validated data.