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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 6, Pages 973–988 (Mi zvmmf10399)  

This article is cited in 7 scientific papers (total in 7 papers)

Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation

E. N. Aristovaab, B. V. Rogovab, A. V. Chikitkinb

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

Abstract: A hybrid scheme is proposed for solving the nonstationary inhomogeneous transport equation. The hybridization procedure is based on two baseline schemes: (1) a bicompact one that is fourth-order accurate in all space variables and third-order accurate in time and (2) a monotone first-order accurate scheme from the family of short characteristic methods with interpolation over illuminated faces. It is shown that the first-order accurate scheme has minimal dissipation, so it is called optimal. The solution of the hybrid scheme depends locally on the solutions of the baseline schemes at each node of the space-time grid. A monotonization procedure is constructed continuously and uniformly in all mesh cells so as to keep fourth-order accuracy in space and third-order accuracy in time in domains where the solution is smooth, while maintaining a high level of accuracy in domains of discontinuous solution. Due to its logical simplicity and uniformity, the algorithm is well suited for supercomputer simulation.

Key words: transport equation, bicompact schemes, short characteristic method, monotone schemes, minimal dissipation, hybrid schemes.

DOI: https://doi.org/10.7868/S004446691606003X

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:6, 962–976

Bibliographic databases:

UDC: 519.63
Received: 09.11.2015

Citation: E. N. Aristova, B. V. Rogov, A. V. Chikitkin, “Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016), 973–988; Comput. Math. Math. Phys., 56:6 (2016), 962–976

Citation in format AMSBIB
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\paper Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation
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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. E. N. Aristova, N. I. Karavaeva, “Bikompaktnye skhemy vysokogo poryadka approksimatsii dlya uravnenii kvazidiffuzii”, Preprinty IPM im. M. V. Keldysha, 2018, 045, 28 pp.  mathnet  crossref  elib
    2. A. V. Chikitkin, B. V. Rogov, “Dva varianta parallelnoi realizatsii vysokotochnykh bikompaktnykh skhem dlya mnogomernogo neodnorodnogo uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2018, 177, 24 pp.  mathnet  crossref  elib
    3. E. N. Aristova, N. I. Karavaeva, “Realizatsiya bikompaktnoi skhemy dlya HOLO algoritmov resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2019, 021, 28 pp.  mathnet  crossref  elib
    4. E. N. Aristova, N. I. Karavaeva, “Postanovka granichnykh uslovii v bikompaktnykh skhemakh dlya HOLO algoritmov resheniya uravneniya perenosa”, Matem. modelirovanie, 31:9 (2019), 3–20  mathnet  crossref  elib
    5. B. V. Rogov, A. V. Chikitkin, “O skhodimosti i tochnosti metoda iteriruemoi priblizhennoi faktorizatsii operatorov mnogomernykh vysokotochnykh bikompaktnykh skhem”, Matem. modelirovanie, 31:12 (2019), 119–144  mathnet  crossref  elib
    6. E. N. Aristova, G. O. Astafurov, “O sravnenii dissipativno-dispersionnykh svoistv nekotorykh konservativnykh raznostnykh skhem”, Preprinty IPM im. M. V. Keldysha, 2020, 117, 22 pp.  mathnet  crossref
    7. E. N. Aristova, N. I. Karavaeva, “Bikompaktnye skhemy dlya chislennogo resheniya modelnoi zadachi nestatsionarnogo perenosa neitronov HOLO algoritmami”, Matem. modelirovanie, 33:8 (2021), 3–26  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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