The Riemann problem for one-dimensional isentropic flow of a mixture of a non-ideal gas with small solid particles

Abstract

We concern with the Riemann problem for one-dimensional inviscid and isentropic flow of a mixture of a non-ideal gas with small solid particles. The expressions of elementary wave curves are established. Besides, we reveal the properties of these wave curves. Furthermore, all kinds of solution patterns to the Riemann problem are shown. Finally, the comparisons between semi-analytical results and numerical results to the Riemann problem are carried out, which are in good agreement with the corresponding theoretical analysis. Keywords: Riemann problem, Dusty gas, Compressible fluid, Numerical simulations