On the 2-D Riemann problem for the compressible Euler equations I. Interaction of shocks and rarefaction waves

We are concerned with the Riemann problem for the two-dimensionalcompressible Euler equations in gas dynamics.The central point at this issue is the dynamical interaction of shock waves,centered rarefaction waves, and contact discontinuities that connect twoneighboring constant initial states in the quadrants.The Riemann problem is classified into eighteen genuinely differentcases. For each configuration, the structure of the Riemann solutionis analyzed using the method of characteristics, andcorresponding numerical solution is illustrated by contour plotsusing an upwind averaging scheme that is second order in the smoothregion of the solution.In the first paperwe mainly focus on the interaction of shocks and rarefaction waves.The theory is developed from an analysis of the structureof the Euler equations and their Riemann solutions in [CC, ZZ]and the MmB scheme [WY].