LAUSR

A theoretical solution of the Riemann problem to the two-phase flow model in non-conservative form of Saurel and Abgrall is presented under the assumption that all the nonlinear waves are shocks. The solution, called 4-shock Riemann solver, is then utilized to construct a path-conservative scheme for numerical solution of a general initial boundary value problem for the two-phase flow model in the non-conservative form. Moreover, a high-order path-conservative scheme of Godunov type is given via the MUSCL reconstruction and the Runge-Kutta technique first in one dimension, based on the 4-shock Riemann solver, and then extended to the two-dimensional case by dimensional splitting. A number of numerical tests are carried out and numerical results demonstrate the accuracy and robustness of our scheme in the numerical solution of the five-equations model for two-phase flow. AMS subject classifications: 35Q53, 35E15, 74C05, 74F10, 74M20