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Zh. Vychisl. Mat. Mat. Fiz., 2000, Volume 40, Number 12, Pages 1857–1874 (Mi zvmmf1410)  

This article is cited in 25 scientific papers (total in 25 papers)

Construction of high-order accurate shock-capturing finite difference schemes for unsteady shock waves

V. V. Ostapenko

M. A. Lavrent'ev Institute of Hydrodynamics, Novosibirsk

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English version:
Computational Mathematics and Mathematical Physics, 2000, 40:12, 1784–1800

Bibliographic databases:
UDC: 519.6:531.33
MSC: Primary 76M20; Secondary 76L05
Received: 06.01.2000

Citation: V. V. Ostapenko, “Construction of high-order accurate shock-capturing finite difference schemes for unsteady shock waves”, Zh. Vychisl. Mat. Mat. Fiz., 40:12 (2000), 1857–1874; Comput. Math. Math. Phys., 40:12 (2000), 1784–1800

Citation in format AMSBIB
\by V.~V.~Ostapenko
\paper Construction of high-order accurate shock-capturing finite difference schemes for unsteady shock waves
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2000
\vol 40
\issue 12
\pages 1857--1874
\jour Comput. Math. Math. Phys.
\yr 2000
\vol 40
\issue 12
\pages 1784--1800

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    1. A. F. Voevodin, V. V. Ostapenko, “O raschete preryvnykh voln v otkrytykh ruslakh”, Sib. zhurn. vychisl. matem., 3:4 (2000), 305–321  mathnet  zmath
    2. V. V. Ostapenko, “Symmetric compact schemes with artificial viscosities of increased order of divergence”, Comput. Math. Math. Phys., 42:7 (2002), 980–999  mathnet  mathscinet  zmath
    3. N. M. Borisova, V. V. Ostapenko, “On accuracy of the shock wave computations by the shock-fitting method”, Comput. Math. Math. Phys., 43:10 (2003), 1437–1458  mathnet  mathscinet  zmath  elib
    4. O. A. Kovyrkina, V. V. Ostapenko, “Construction of asymptotics of a discrete solution based on nonclassical differential approximations”, Comput. Math. Math. Phys., 45:1 (2005), 83–103  mathnet  mathscinet  zmath  elib  elib
    5. N. M. Borisova, V. V. Ostapenko, “Numerical simulation of discontinuous waves propagating over a dry bed”, Comput. Math. Math. Phys., 46:7 (2006), 1254–1276  mathnet  crossref  mathscinet
    6. A. S. Ovcharova, “Leveling a capillary ridge generated by substrate geometry”, Comput. Math. Math. Phys., 46:2 (2006), 305–314  mathnet  crossref  mathscinet  zmath
    7. V. V. Ostapenko, “O monotonnosti balansno-kharakteristicheskoi skhemy”, Matem. modelirovanie, 21:7 (2009), 29–42  mathnet  mathscinet
    8. Ostapenko V., “On Convergence of High Order Shock Capturing Difference Schemes”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1301, 2010, 413–425  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Louaked M., Tounsi H., “Well-balanced Component-wise Scheme for Shallow Water System”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1301, 2010, 404–412  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. Ostapenko V.V., “On the construction of compact difference schemes”, Doklady Mathematics, 84:3 (2011), 841–845  crossref  mathscinet  zmath  isi  elib  elib  scopus
    11. V. V. Ostapenko, “On compact approximations of divergent differential equations”, Num. Anal. Appl., 5:3 (2012), 242–253  mathnet  crossref  elib
    12. Rogov B.V., “High-Order Accurate Running Compact Scheme for Multidimensional Hyperbolic Equations”, Dokl. Math., 86:1 (2012), 582–586  crossref  mathscinet  zmath  isi  elib  elib  scopus
    13. B. V. Rogov, “High-order accurate monotone compact running scheme for multidimensional hyperbolic equations”, Comput. Math. Math. Phys., 53:2 (2013), 205–214  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. Ovcharova A.S., “Rupture of Liquid Film, Placed Over Deep Fluid, Under Action of Thermal Load”, Int. J. Heat Mass Transf., 78 (2014), 294–301  crossref  isi  elib  scopus
    15. N. A. Mikhailov, “On convergence rate of WENO schemes behind a shock front”, Math. Models Comput. Simul., 7:5 (2015), 467–474  mathnet  crossref  elib
    16. V. V. Ostapenko, A. V. Speshilova, A. A. Cherevko, A. P. Chupakhin, “Numerical simulation of wave motions on a rotating attracting spherical zone”, Comput. Math. Math. Phys., 55:3 (2015), 470–486  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. N. A. Zyuzina, V. V. Ostapenko, “Modification of the Cabaret scheme ensuring its high accuracy on local extrema”, Math. Models Comput. Simul., 8:3 (2016), 231–237  mathnet  crossref  elib
    18. Ostapenko V. Kovyrkina O., “On Construction of Combined Shock-Capturing Finite-Difference Schemes of High Accuracy”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, ed. Dimov I. Farago I. Vulkov L., Springer International Publishing Ag, 2017, 525–532  crossref  mathscinet  zmath  isi  scopus
    19. Kovyrkina O.A. Ostapenko V.V., “On the Construction of Combined Finite-Difference Schemes of High Accuracy”, Dokl. Math., 97:1 (2018), 77–81  crossref  mathscinet  zmath  isi  scopus
    20. M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, V. F. Tishkin, “Issledovanie tochnosti razryvnogo metoda Galerkina pri raschete reshenii s udarnymi volnami”, Preprinty IPM im. M. V. Keldysha, 2018, 195, 20 pp.  mathnet  crossref  elib
    21. Kovyrkina O. Ostapenko V., “High Order Combined Finite-Difference Schemes”, International Conference of Numerical Analysis and Applied Mathematics (Icnaam 2017), AIP Conference Proceedings, 1978, Amer Inst Physics, 2018, UNSP 470027-1  crossref  isi  scopus
    22. M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, V. F. Tishkin, “On the accuracy of the discontinuous Galerkin method in calculation of shock waves”, Comput. Math. Math. Phys., 58:8 (2018), 1344–1353  mathnet  crossref  crossref  isi  elib
    23. O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws”, Comput. Math. Math. Phys., 58:9 (2018), 1435–1450  mathnet  crossref  crossref  isi  elib
    24. Ostapenko V.V. Khandeeva N.A., “The Accuracy of Finite-Difference Schemes Calculating the Interaction of Shock Waves”, Dokl. Phys., 64:4 (2019), 197–201  crossref  isi
    25. O. A. Kovyrkina, V. V. Ostapenko, “O tochnosti skhemy tipa MUSCL pri raschete razryvnykh reshenii”, Matem. modelirovanie, 33:1 (2021), 105–121  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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