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Two-Layer Completely Conservative Difference Schemes for the Gasdynamic Equations in Eulerian Coordinates with Adaptive Solution Regularization

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Abstract

A family of two-layer completely conservative difference schemes with space-profiled weight factors for approximations on a time grid is constructed for the gasdynamic equations in Eulerian coordinates. We propose a construction for regularized mass, momentum, and internal-energy fluxes that effectively removes nonphysical solution oscillations and does not violate the complete conservativeness of the difference schemes in this class.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia

    Yu. A. Poveshchenko, V. A. Gasilov, V. O. Podryga & Yu. S. Sharova

  2. Moscow Automobile and Road Construction State Technical University (MADI), Moscow, 125319, Russia

    V. O. Podryga

  3. Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700, Russia

    O. R. Rehimly

Authors
  1. Yu. A. Poveshchenko
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  2. V. A. Gasilov
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  3. V. O. Podryga
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  4. O. R. Rehimly
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  5. Yu. S. Sharova
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Corresponding authors

Correspondence to Yu. A. Poveshchenko, V. A. Gasilov, V. O. Podryga, O. R. Rehimly or Yu. S. Sharova.

Additional information

Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 7, pp. 1009–1022.

Funding

This work was supported by Russian Science Foundation, project no. 17-71-20118.

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Poveshchenko, Y.A., Gasilov, V.A., Podryga, V.O. et al. Two-Layer Completely Conservative Difference Schemes for the Gasdynamic Equations in Eulerian Coordinates with Adaptive Solution Regularization. Diff Equat 55, 976–989 (2019). https://doi.org/10.1134/S0012266119070103

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  • DOI: https://doi.org/10.1134/S0012266119070103

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