Application of Osher and PRICE-C schemes to solve compressible isothermal two-fluid models of two-phase flow

In this paper, two path-conservative schemes, namely Osher and PRICE-C schemes have been used to solve isothermal compressible two-phase flows using four-equation model. Path-Conservative Osher (PC-Osher) scheme is an upwind method using the full eigenstructure of the system but PRICE-C scheme is a central method, in which using the full eigenstructure of the system is not necessary. Different two-phase flow problems are solved using these schemes and their results are compared. The numerical efficiency of two schemes and their abilities in the simulation of near single phase flows are also examined. The extension of these schemes to the second order of accuracy is performed using the well-known TVD-MUSCL-Hancock (TMH) method. The results show that for the same level of accuracy, the PC-Osher is more efficient than the PRICE-C scheme in view of computational time. However, the PC-Osher scheme fails to predict near single phase flows compared to the PRICE-C scheme. The results also show that the second order extension of both schemes is less diffusive on the sonic waves while they show small amplitude oscillations on the volume fraction waves.