Comparisons of upwind numerical scheme for a hyperbolic two-fluid model

A lot of upwind scheme has been developed for simulating high speed, single-phase flows and some of them prove to be very successful. However, all of these numerical schemes cannot be applied for two-phase flow problems due to their complexity relating the interfacial phenomena between two phases of fluid. For this reason, sometimes we need to find an optimal numerical scheme in order to adopt a prominent upwind scheme to the hyperbolic two-fluid model for two-phase flows. Before choosing an upwind numerical scheme, we need to compare some candidates by solving benchmark problems. In this study, we compare the Flux Vector Splitting (FVS) scheme with the Harten, Lax and van Leer (HLL) scheme for a hyperbolic two-fluid model for 1D. equation system and analyze their advantage and disadvantage by calculating the two-phase shock-tube problem.