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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 7, Pages 1196–1207 (Mi zvmmf10237)  

This article is cited in 1 scientific paper (total in 1 paper)

Hybrid running schemes with upwind and bicompact symmetric differencing for hyperbolic equations

M. D. Bragina, B. V. Rogovab

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

Abstract: New hybrid difference schemes are proposed for computing discontinuous solutions of hyperbolic equations. Involved in these schemes, a bicompact scheme that is third-order accurate in time and fourth-order accurate in space is monotonized using several partner schemes, namely, a first-order accurate explicit upwind scheme and two bicompact schemes of second and fourth orders of accuracy in space, both of the first order of accuracy in time. Their total domain of monotonicity covers all Courant numbers. An algorithm for automatically choosing the most suitable partner scheme is constructed. The mechanism of switching between high- and low-order accurate schemes is rigorously substantiated. All the schemes used can be efficiently implemented by applying the running calculation method. The hybrid schemes proposed have been tested on a model two-dimensional explosion problem in an ideal gas.

Key words: hyperbolic equations, discontinuous solutions, hybrid schemes, high-order accurate compact and bicompact schemes, numerical solution of explosion problem in ideal gas.

DOI: https://doi.org/10.7868/S0044466915070042

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:7, 1177–1187

Bibliographic databases:

Document Type: Article
UDC: 519.633
Received: 16.06.2014

Citation: M. D. Bragin, B. V. Rogov, “Hybrid running schemes with upwind and bicompact symmetric differencing for hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015), 1196–1207; Comput. Math. Math. Phys., 55:7 (2015), 1177–1187

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. D. Bragin, B. V. Rogov, “Minimal dissipation hybrid bicompact schemes for hyperbolic equations”, Comput. Math. Math. Phys., 56:6 (2016), 947–961  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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