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Classification of the Riemann problem for two-dimensional gas dynamics

by C. W. Schulz-Rinne

(Report number 1991-05)

Abstract
The Riemann problem for two-dimensional gas dynamics with isentropic and polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states. With this restriction the existence of sixteen (resp. fifteen) genuinely different wave combinations for isentropic (resp. polytropic) gas is proved. For each configuration the relations for the initial data and the symmetry properties of the solution are given. This paper corrects the conjectured classification presented in T. Zhang and Y. Zheng, SIAM J. Math. Anal. 21 (1990) 593-630.

Keywords: Riemann problem, gas dynamics, initial data, compatibility conditions, self-similar solution

BibTeX

@Techreport{S91_5,
  author = {C. W. Schulz-Rinne},
  title = {Classification of the Riemann problem for two-dimensional gas dynamics},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1991-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1991/1991-05.pdf },
  year = {1991}
}

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