Classification of the Riemann problem for compressible two-dimensional Euler system in non-ideal gas

Abstract

This work is devoted to the study of two-dimensional Riemann problem modeled by compressible Euler system for the non-ideal gas. The initial constant data are divided in four quadrants in such a way that only one planar elementary wave connects two neighboring states. We classify the different combinations of planar elementary waves and subsequently discuss one by one using the method of generalized characteristic analysis. Attention is drawn to the changes in elementary waves, with regard to their shape, speed and strength, under the influence of the van der Waals parameter b. It has been shown that only sixteen (respectively, fifteen) distinct combinations of planar elementary waves exist for isentropic (respectively, non-isentropic) non-ideal gas flows.