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Doklady Mathematics

, Volume 98, Issue 2, pp 506–510 | Cite as

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

  • N. A. Zyuzina
  • O. A. Kovyrkina
  • V. V. Ostapenko
Mathematics
  • 1 Downloads

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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References

  1. 1.
    S. K. Godunov, Mat. Sb. 47 (3), 271–306 (1959).MathSciNetGoogle Scholar
  2. 2.
    B. Van Leer, J. Comput. Phys. 32 (1), 101–136 (1979).MathSciNetCrossRefGoogle Scholar
  3. 3.
    A. Harten, J. Comput. Phys. 49, 357–393 (1983).MathSciNetCrossRefGoogle Scholar
  4. 4.
    H. Nessyahu and E. Tadmor, J. Comput. Phys. 87 (2), 408–463 (1990).MathSciNetCrossRefGoogle Scholar
  5. 5.
    G. S. Jiang and C. W. Shu, J. Comput. Phys. 126, 202–228 (1996).MathSciNetCrossRefGoogle Scholar
  6. 6.
    V. M. Goloviznin, M. A. Zaitsev, S. A. Karabasov, and I. A. Korotkin, New CFD Algorithms for Multiprocessor Computer Systems (Mosk. Gos. Univ., Moscow, 2013) [in Russian].Google Scholar
  7. 7.
    V. V. Ostapenko, Comput. Math. Math. Phys. 37 (10), 1161–1172 (1997).MathSciNetGoogle Scholar
  8. 8.
    J. Casper and M. H. Carpenter, SIAM J. Sci. Comput. 19 (1), 813–828 (1998).MathSciNetCrossRefGoogle Scholar
  9. 9.
    V. V. Ostapenko, Comput. Math. Math. Phys. 40 (12), 1784–1800 (2000).MathSciNetGoogle Scholar
  10. 10.
    O. A. Kovyrkina and V. V. Ostapenko, Dokl. Math. 82 (1), 599–603 (2010).MathSciNetCrossRefGoogle Scholar
  11. 11.
    O. A. Kovyrkina and V. V. Ostapenko, Math. Models Comput. Simul. 6 (2), 183–191 (2014).MathSciNetCrossRefGoogle Scholar
  12. 12.
    N. A. Mikhailov, Math. Models Comput. Simul. 7 (5), 467–474 (2015).MathSciNetCrossRefGoogle Scholar
  13. 13.
    V. V. Ostapenko, Comput. Math. Math. Phys. 38 (8), 1299–1311 (1998).MathSciNetGoogle Scholar
  14. 14.
    O. A. Kovyrkina and V. V. Ostapenko, Dokl. Math. 97 (1), 77–81 (2018).CrossRefGoogle Scholar
  15. 15.
    V. V. Rusanov, Dokl. Akad. Nauk SSSR 180 (6), 1303–1305 (1968).MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • N. A. Zyuzina
    • 1
    • 2
  • O. A. Kovyrkina
    • 1
  • V. V. Ostapenko
    • 1
  1. 1.Lavrent’ev Institute of Hydrodynamics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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