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The exact solution of the generalized Riemann problem in the curved geometries

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Abstract

In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem from the conventional setting of a planar shock-interface interaction.

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Correspondence to Ju Hong Kim.

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Kim, J.H. The exact solution of the generalized Riemann problem in the curved geometries. Korean J. Comput. & Appl. Math. 7, 271 (2000). https://doi.org/10.1007/BF03012193

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AMS Mathematics Subject Classification

  • 76N15
  • 76L05

Key word and phrases

  • Shock-interaction
  • Euler equation
  • asymptotic expansion
  • generalized Riemann problem