Singular surface for non-ideal two-phase modified Chaplygin flow consisting of source term

Abstract

In this manuscript, a system of partial differential equations (PDEs) outlining one-dimensional isentropic two-phase flow model consisting of a non-constant source term with non-ideal modified Chaplygin gas is derived. The model is reduced to an equivalent system of ordinary differential equations (ODEs) via Lie group scheme. The transport equation for the singular surface is derived using the compatibility conditions and solved numerically by coupling with the system of ODEs. Further, the effects of inclination of the flow and non-idealness on the amplitude of steepened wave (or singular surface) are investigated.