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On L2-Dissipativity of a Linearized Explicit Finite-Difference Scheme with Quasi-Gasdynamic Regularization for the Barotropic Gas Dynamics System of Equations

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Abstract

We study an explicit two-level symmetric (in space) finite-difference scheme for the multidimensional barotropic gas dynamics system of equations with quasi-gasdynamic regularization linearized at a constant solution (with an arbitrary velocity). A criterion and both necessary and sufficient conditions for the L2-dissipativity of the solutions to the Cauchy problem for the scheme are derived by the spectral method. In them, the Courant number is uniformly bounded with respect to the Mach number.

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Funding

This work was supported by the Russian Science Foundation, project no. 19-11-00169.

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Authors and Affiliations

  1. National Research University Higher School of Economics, 109028, Moscow, Russia

    A. A. Zlotnik & T. A. Lomonosov

  2. Federal Research Center Keldysh Institute of Applied Mathmatics, Russian Academy of Sciences, 125047, Moscow, Russia

    A. A. Zlotnik

Authors
  1. A. A. Zlotnik
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  2. T. A. Lomonosov
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Corresponding authors

Correspondence to A. A. Zlotnik or T. A. Lomonosov.

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Translated by I. Ruzanova

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Zlotnik, A.A., Lomonosov, T.A. On L2-Dissipativity of a Linearized Explicit Finite-Difference Scheme with Quasi-Gasdynamic Regularization for the Barotropic Gas Dynamics System of Equations. Dokl. Math. 101, 198–204 (2020). https://doi.org/10.1134/S1064562420030229

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