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Monotone approximation of a scalar conservation law based on the CABARET scheme in the case of a sign-changing characteristic field

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Abstract

The monotonicity of the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux is analyzed. Monotonicity conditions for this scheme are obtained in domains where the propagation velocity of characteristics of the approximated conservative equation is of constant sign and near sonic lines, at which the propagation velocity of characteristics changes its sign. Test computations illustrating these properties of the CABARET scheme are presented.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    N. A. Zyuzina & V. V. Ostapenko

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    V. V. Ostapenko

Authors
  1. N. A. Zyuzina
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  2. V. V. Ostapenko
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Correspondence to N. A. Zyuzina.

Additional information

Original Russian Text © N.A. Zyuzina, V.V. Ostapenko, 2016, published in Doklady Akademii Nauk, 2016, Vol. 470, No. 4, pp. 375–379.

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Zyuzina, N.A., Ostapenko, V.V. Monotone approximation of a scalar conservation law based on the CABARET scheme in the case of a sign-changing characteristic field. Dokl. Math. 94, 538–542 (2016). https://doi.org/10.1134/S1064562416050185

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  • DOI: https://doi.org/10.1134/S1064562416050185

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