Preprint 2000-037

Solution of Two-Dimensional Riemann Problems for Gas Dynamics

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 which 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 in \cite{KNP2}. 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.

Paper:

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Author(s):

Alexander Kurganov, <kurganov@math.lsa.umich.edu>

Eitan Tadmor, <tadmor@math.ucla.edu>

Publishing information:

Comments:

A pdf version is available

Submitted by:

<tadmor@math.ucla.edu> September 12 2000.