Solution of two‐dimensional Riemann problems for gas dynamics without Riemann problem solvers

Abstract 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 configurations, the 2‐D case consists of a plethora of geometric wave patterns that pose a computational challenge for high‐resolution methods. The main feature in the present computations of these 2‐D waves is the use of the Riemann‐solvers‐free central schemes presented by Kurganov et al. This family of central schemes avoids the intricate and time‐consuming computation of the eigensystem of the problem and hence offers 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. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 584–608, 2002