On the interactions of arbitrary shocks in isentropic drift-flux model of two-phase flows

In this article, we consider the wave interactions for a 3x3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3 \times 3$$\end{document} system of conservation laws governing the isentropic drift-flux model of two-phase flows. Here, we express the elementary waves as a one-parameter family of curves. Further, we reduce the system of equations by taking the projection of these elementary wave curves into the phase plane using the properties of Riemann invariants. Consequently, we establish that the interactions of two shocks of the same family with arbitrary strengths produce a rarefaction wave of different families. Finally, we discuss the Riemann solution after the interactions.