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Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws

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Abstract

A method is proposed for constructing a CABARET scheme that approximates a hyperbolic system of conservation laws that cannot be written in the form of invariants. This technique is based on the method of quasi-invariants and additional flux correction, which ensures monotonization of the difference solution in calculating discontinuous solutions with shock waves and contact discontinuities. As an example, a system of conservation laws for nonisentropic gas dynamics with a polytropic equation of state is considered. Test calculations of the Blast Wave initial-boundary value problem showed that the proposed scheme suppresses nonphysical oscillations leading to the instability of the difference solution in the case when the CABARET scheme is used without additional flux correction.

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Funding

This work was supported in part by the Russian Foundation for Basic Research and the National Natural Science Foundation of China, project no. 21-51-53012.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    V. V. Ostapenko

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    V. V. Ostapenko & V. A. Kolotilov

  3. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    V. A. Kolotilov

Authors
  1. V. V. Ostapenko
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  2. V. A. Kolotilov
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Correspondence to V. V. Ostapenko or V. A. Kolotilov.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Ostapenko, V.V., Kolotilov, V.A. Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws. Dokl. Math. 104, 369–373 (2021). https://doi.org/10.1134/S1064562421060120

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  • DOI: https://doi.org/10.1134/S1064562421060120

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