Interaction of an acceleration wave with a characteristic shock in two-phase real modified Chaplygin model containing a variable source term

In this manuscript, a mathematical model describing isentropic two-phase real modified Chaplygin flow with a non-constant source term has been considered. The model governed by the system of partial differential equations (PDEs) is reduced into an equivalent system of ordinary differential equations (ODEs) via Lie-symmetry analysis. The transport equations for the characteristic shock and acceleration wave are derived to analyze their evolutionary behavior and solved numerically along with the system of ODEs. Special attention is devoted to investigate the effects of non-idealness and source term on the progression of characteristic shock and acceleration wave. Moreover, the amplitude of the reflected wave, transmitted wave and jump in the acceleration of shock, generated from the interaction of characteristic with acceleration wave, are computed.