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Numerical solution of the Riemann problem for two-fimensional gas dynamics

by C. W. Schulz-Rinne and J. P. Collins and M. Glaz

(Report number 1992-02)

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 sixteen (resp. fifteen) genuinely different wave combinations for isentropic (resp. polytropic) gas exist. For each configuration the numerical solution is analyzed and illustrated by contour plots. Additionally, the required relations for the initial data and the symmetry properties of the solutions are given. The chosen calculations correspond closely to the cases studied by T. Zhang and Y. Zheng, SIAM J. Math. Anal. 21 (1990), 593-630, so that the analytical theory can be directly compared to our numerical study.

Keywords: Riemann problem, gas dynamics, Godunov method, wave interaction

@Techreport{SCG92_12,
  author = {C. W. Schulz-Rinne and J. P. Collins and M. Glaz},
  title = {Numerical solution of the Riemann problem for two-fimensional gas dynamics},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1992-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1992/1992-02.pdf },
  year = {1992}
}

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