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Investigation of the stability and convergence of difference schemes for a polytropic gas with subsonic flows

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Abstract

We analyze the stability with respect to the initial data and the convergence in the uniform norm of difference schemes approximating the equations of a polytropic gas in terms of the Riemann invariants. We obtain conditions on the initial data providing the presence of only subsonic flows and the absence of shock waves in the medium in the course of time. We discuss the relationship between the notions of stability and monotonicity of difference schemes for nonlinear problems. We present the results of a numerical experiment that justify the obtained theoretical conclusions.

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Authors and Affiliations

  1. Institute for Mathematics, National Academy of Sciences, Minsk, Belarus

    P. P. Matus & M. M. Chuiko

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  1. P. P. Matus
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  2. M. M. Chuiko
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Dedicated to the ninetieth birthday of Academician Aleksandr Andreevich Samarskii

Original Russian Text © P.P. Matus, M.M. Chuiko, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 7, pp. 1053–1064.

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Matus, P.P., Chuiko, M.M. Investigation of the stability and convergence of difference schemes for a polytropic gas with subsonic flows. Diff Equat 45, 1074–1085 (2009). https://doi.org/10.1134/S0012266109070143

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  • DOI: https://doi.org/10.1134/S0012266109070143

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