The analytical solutions to one-dimensional non-ideal dusty gas flow

This paper is concerned with the analytical solutions to the Riemann problem for one-dimensional non-ideal dusty gas flow. We obtain explicitly the elementary wave curves to one-dimensional non-ideal dusty gas flow, and analyze the properties of these wave curves. On the basis of these preparations, by rigorously analyzing the uniqueness and existence of the solution to a system of two nonlinear equations, the analytical solutions are obtained. Besides, the corresponding numerical solutions are also provided. It is shown that the analytical solutions are identical with the corresponding numerical solutions.