A coupled approach to compute approximate solutions of a compressible immiscible three-phase flow model with fast transient and stiff source terms

This paper aims at developing a new numerical coupled approach to compute solutions of a compressible immiscible three-phase flow model with stiff source terms. The targeted applications involve flows with fast transient and shock waves. Thus, a well-posed model with respect to the initial conditions that embarks an entropy inequality is considered. A preliminary work on the underlying relaxation process of the model is conducted. Then the new numerical scheme is presented and numerically tested.