Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin Gasdynamics

The motivation of the present study is to derive the solution of the Riemann problem for modified Chaplygin gas equations in the presence of constant external force. The analysis leads to the fact that in some special circumstances delta shock appears in the solution of the Riemann problem. Also, the Rankine-Hugoniot relations for delta shock wave which are utilized to determine the strength, position and propagation speed of the delta shocks have been derived. Delta shock wave solution to the Riemann problem for the modified Chaplygin gas equation is obtained. It is found that the external force term, appearing in the governing equations, influences the Riemann solution for the modified Chaplygin gas equation.