Title:  Some progresses on two-dimensional Riemann problems in gas dynamics

Abstract:  Two dimensional Riemann problems for compressible fluid flows assume the simplest piecewise sectorial initial state but provide the most fundamental wave configurations, including the reflection of oblique shocks and vortex-shock interaction etc. In this talk I will show many fascinating pictures, based on 2D Riemann solutions, to disclose the mysteries of compressible fluid world both through analytical tools (in the form of mathematical theorems) and computational techniques (in the form of simulations). The analysis is based on the characteristic decomposition theory we developed recently, while the simulations are obtained using the generalized Riemann problem (GRP) scheme that is equipped with a highly accurate solver in the construction of numerical fluxes by a way of tracking singularities analytically and keeping entropy exactly computed.