Solution of Two-Dimensional Riemann Problems for Gas Dynamics without Riemann Problem Solvers

We report here on our numerical study of the two-dimensional Riemann problem for the compressible Euler equations. Compared with the relatively simple 1-D con gurations, the 2-D case consists of a plethora of geometric wave patterns which pose a computational challenge for highresolution methods. The main feature in the present computations of these 2-D waves is the use of the Riemann-solvers-free central schemes presented in [10]. This family of central schemes avoids the intricate and time-consuming computation of the eigensystem of the problem, and hence o ers a considerably simpler alternative to upwind methods. The numerical results illustrate that despite their simplicity, the central schemes are able to recover with comparable high-resolution, the various features observed in the earlier, more expensive computations. AMS subject classi cation: Primary 65M10; Secondary 65M05