Evolution of characteristic shocks in two-phase modified Chaplygin flow consisting of source term

This manuscript presents a system of partial differential equations (PDEs) governed by the isentropic two-phase flow model with modified Chaplygin equation of state consisting of a non-constant source term in one-dimension. Lie symmetry analysis is employed to reduce the governing system into an equivalent system of ordinary differential equations (ODEs). The patterns of flow variables and the effects of source term parameters are investigated graphically. Further, the transport equation for the evolution of characteristic shocks is derived and solved numerically using an exact solution of the system under consideration. Also, the effects of inclination of flow and acceleration due to gravity on the behavior of the characteristic shock are analyzed.