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Combined DG Scheme That Maintains Increased Accuracy in Shock Wave Areas

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Abstract

A combined scheme for the discontinuous Galerkin (DG) method is proposed. This scheme monotonically localizes the fronts of shock waves and simultaneously maintains increased accuracy in the regions of smoothness of the computed weak solutions. In this scheme, a nonmonotone version of the third-order DG method is used as a baseline scheme and a monotone version of this method is used as an internal scheme, in which a nonlinear correction of numerical fluxes is used. Tests demonstrate the advantages of the new scheme as compared to standard monotonized variants of the DG method.

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Funding

This work was supported by the Russian Science Foundation, grant no. 16-11-10033.

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Authors and Affiliations

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

    M. E. Ladonkina, O. A. Nekliudova &  V. F. Tishkin

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

    M. E. Ladonkina, O. A. Nekliudova, V. V. Ostapenko &  V. F. Tishkin

  3. Novosibirsk State University, 630090, Novosibirsk, Russia

    V. V. Ostapenko

Authors
  1. M. E. Ladonkina
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  2. O. A. Nekliudova
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  3. V. V. Ostapenko
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  4. V. F. Tishkin
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Corresponding author

Correspondence to V. V. Ostapenko.

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Translated by I. Ruzanova

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Ladonkina, M.E., Nekliudova, O.A., Ostapenko, V.V. et al. Combined DG Scheme That Maintains Increased Accuracy in Shock Wave Areas. Dokl. Math. 100, 519–523 (2019). https://doi.org/10.1134/S106456241906005X

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  • DOI: https://doi.org/10.1134/S106456241906005X

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