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Accuracy of MUSCL-Type Schemes in Shock Wave Calculations

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Abstract

The central-difference Nessyahu–Tadmor (NT) scheme is considered, which is built using second-order MUSCL reconstruction of fluxes. The accuracy of the NT scheme is studied as applied to calculating shock waves propagating with a variable velocity. It is shown that this scheme has the first order of integral convergence on intervals with one of the boundaries lying in the region of influence of the shock wave. As a result, the local accuracy of the NT scheme is significantly reduced in these areas. Test calculations are presented that demonstrate these properties of the NT scheme.

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REFERENCES

  1. S. K. Godunov, Mat. Sb. 47 (3), 271–306 (1959).

    MathSciNet  Google Scholar 

  2. B. Van Leer, J. Comput. Phys. 32 (1), 101–136 (1979). https://doi.org/10.1016/0021-9991(79)90145-1

    Article  Google Scholar 

  3. A. Harten, J. Comput. Phys. 32 (1), 101–136 (1983). https://doi.org/10.1016/0021-9991(83)90136-5

    Article  Google Scholar 

  4. A. Harten and S. Osher, SIAM J. Numer. Anal. 24 (2), 279–309 (1987). https://doi.org/10.1007/978-3-642-60543-7_11

    Article  MathSciNet  Google Scholar 

  5. G. S. Jiang and C. W. Shu, J. Comput. Phys. 126, 202–228 (1996). https://doi.org/10.1006/jcph.1996.0130

    Article  MathSciNet  Google Scholar 

  6. B. Cockburn, Lect. Notes Math. 1697, 151–268 (1998). https://doi.org/10.1007/BFb0096353

    Article  Google Scholar 

  7. S. A. Karabasov and V. M. Goloviznin, J. Comput. Phys. 228, 7426–7451 (2009). https://doi.org/10.1016/j.jcp.2009.06.037

    Article  MathSciNet  Google Scholar 

  8. O. A. Kovyrkina and V. V. Ostapenko, Dokl. Math. 82 (1), 599–603 (2010). https://doi.org/10.1134/S1064562410040265

    Article  MathSciNet  Google Scholar 

  9. N. A. Mikhailov, Math. Models Comput. Simul. 7 (5), 467–474 (2015). https://doi.org/10.1134/S2070048215050075

    Article  MathSciNet  Google Scholar 

  10. M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, and V. F. Tishkin, Comput. Math. Math. Phys. 58 (8), 1344–1353 (2018). https://doi.org/10.1134/S0965542518080122

    Article  MathSciNet  Google Scholar 

  11. O. A. Kovyrkina and V. V. Ostapenko, Vychisl. Tekhnol. 23 (2), 37–54 (2018).

    Google Scholar 

  12. H. Nessyahu and E. Tadmor, J. Comput. Phys. 87 (2), 408–463 (1990).

    Article  MathSciNet  Google Scholar 

  13. A. Kurganov and E. Tadmor, J. Comput. Phys. 160 (1), 241–282 (2000). https://doi.org/10.1006/jcph.2000.6459

    Article  MathSciNet  Google Scholar 

  14. N. A. Zyuzina, O. A. Kovyrkina, and V. V. Ostapenko, Dokl. Math. 98 (2), 506–510 (2018). https://doi.org/10.1134/S1064562418060315

    Article  Google Scholar 

Download references

Funding

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

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Science, 630090, Novosibirsk, Russia

    O. A. Kovyrkina & V. V. Ostapenko

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    V. V. Ostapenko

Authors
  1. O. A. Kovyrkina
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  2. V. V. Ostapenko
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Corresponding authors

Correspondence to O. A. Kovyrkina or V. V. Ostapenko.

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Translated by I. Ruzanova

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Kovyrkina, O.A., Ostapenko, V.V. Accuracy of MUSCL-Type Schemes in Shock Wave Calculations. Dokl. Math. 101, 209–213 (2020). https://doi.org/10.1134/S1064562420030126

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  • DOI: https://doi.org/10.1134/S1064562420030126

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