On two-dimensional Riemann problem for pressure-gradient equations of the Euler system
The authors consider the two-dimensional Riemann problem for the pressure-gradient equations with four pieces of initial data, which are restricted in such a way that only elementary waves appear at each interface. This model, which comes from the flux-splitting of the compressible Euler system, exhibits simpler patterns that in the complete Euler system. Therefore it makes it possible to clarify interactions of waves in two dimensions. In the present paper the authors analyze the structure of solutions and present numerical results to the two-dimensional Riemann problem. The results show that the slip lines have little influence on the structure of solutions, thus the interaction of rarefactions waves and shocks can be studied thoroughly. The authors give a criterion of transition from the regular reflection shock to the Mach reflection shock.
interaction of rarefactions waves and shocks
scientific article; zbMATH DE number 1492546