The analytical solutions of the Riemann problem to 1-D non-ideal flow of dusty gas with external force

Abstract

This work focuses on the analytical solution to the Riemann problem (RP) for a 1-D non-ideal flow of dusty gas with external force. Here it is presumed that external force is a continuous function of time. We explicitly obtain the elementary wave curves to 1-D non-ideal flow of dusty gas with external force and determine these wave curves in form of characteristics. Exhaustive calculations were performed for the elementary wave solutions, such as the rarefaction wave, shock wave, and contact discontinuity. We examine the influence of dust particles on density, velocity of flow, and shock speed and their implications on the solution of RP. Also, the implication of addition of external force is that all solutions are not self similar.