Title: Some progresses on two-dimensional Riemann problems in gas dynamics
Abstract: Two dimensional Riemann problems for compressible 铿倁id 铿俹ws assume the simplest piecewise sectorial initial state but provide the most fundamental wave con铿乬urations, including the re铿俥ction 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 铿倁id 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 铿倁xes by a way of tracking singularities analytically and keeping entropy exactly computed.