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Monotone Finite-Difference Scheme Preserving High Accuracy in Regions of Shock Influence

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Abstract

An explicit combined shock-capturing finite-difference scheme is constructed that localizes shock fronts with high accuracy and simultaneously preserves the high order of convergence in all domains where the computed weak solutions are smooth. In this scheme, Rusanov’s explicit nonmonotone scheme of the third order is used as a basis one, while the internal scheme is based on the second-order monotone CABARET. The advantages of the new scheme as compared with the WENO scheme of the fifth order in space and third order in time are demonstrated in test computations.

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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, O. A. Kovyrkina & V. V. Ostapenko

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    N. A. Zyuzina

Authors
  1. N. A. Zyuzina
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  2. O. A. Kovyrkina
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  3. V. V. Ostapenko
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Corresponding author

Correspondence to V. V. Ostapenko.

Additional information

Original Russian Text © N.A. Zyuzina, O.A. Kovyrkina, V.V. Ostapenko, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 6.

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Zyuzina, N.A., Kovyrkina, O.A. & Ostapenko, V.V. Monotone Finite-Difference Scheme Preserving High Accuracy in Regions of Shock Influence. Dokl. Math. 98, 506–510 (2018). https://doi.org/10.1134/S1064562418060315

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  • DOI: https://doi.org/10.1134/S1064562418060315

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