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Stability of difference schemes in terms of Riemann invariants for a polytropic gas

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Abstract

The monotonicity and stability of a finite difference scheme with respect to initial data in the supremum norm are analyzed as applied to the polytropic gas equations written in terms of Rie-mann invariants for subsonic flows with 1 < γ < 3. Conditions on the initial and boundary data are obtained under which subsonic flows with no shock waves develop in the medium. The theoretical conclusions are supported by numerical results.

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Authors and Affiliations

  1. Institute for Mathematics, National Academy of Sciences, ul. Surganova 11, Minsk, 220072, Belarus

    G. L. Marcinkiewicz & M. M. Chuiko

  2. The John Paul II Catholic University of Lublin, Al. Raclawickie 14, 20-950, Lublin, Poland

    P. P. Matus

Authors
  1. G. L. Marcinkiewicz
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  2. P. P. Matus
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  3. M. M. Chuiko
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Correspondence to G. L. Marcinkiewicz.

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Original Russian Text © G.L. Marcinkiewicz, P.P. Matus, M.M. Chuiko, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 6, pp. 1078–1091.

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Marcinkiewicz, G.L., Matus, P.P. & Chuiko, M.M. Stability of difference schemes in terms of Riemann invariants for a polytropic gas. Comput. Math. and Math. Phys. 50, 1024–1037 (2010). https://doi.org/10.1134/S0965542510060096

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  • DOI: https://doi.org/10.1134/S0965542510060096

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