A Second-Order Path-Conservative Method for the Compressible Non-Conservative Two-Phase Flow (Communications in Computational Physics, 2018)
A theoretical solution of the Riemann problem to the two-phase flow modelin non-conservative form of Saurel and Abgrall is presented under the assumption thatall the nonlinear waves are shocks. The solution, called 4-shock Riemann solver, is thenutilized to construct a path-conservative scheme for numerical solution of a generalinitial boundary value problem for the two-phase flow model in the non-conservativeform.Moreover, a high-order path-conservative scheme of Godunov type is given via theMUSCL reconstruction and the Runge-Kutta technique first in one dimension, basedon 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 resultsdemonstrate the accuracy and robustness of our scheme in the numerical solution ofthe five-equations model for two-phase flow.