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

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 6, Pages 973–988
DOI: https://doi.org/10.7868/S004446691606003X (Mi zvmmf10399)

This article is cited in 15 scientific papers (total in 15 papers)

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

E. N. Aristova^ab, B. V. Rogov^ab, A. V. Chikitkin^b

^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

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

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.

Received: 09.11.2015

English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 6, Pages 962–976
DOI: https://doi.org/10.1134/S0965542516060038

Bibliographic databases:

Document Type: Article

UDC: 519.63

Language: Russian

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

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This publication is cited in the following 15 articles:

E. N. Aristova, N. I. Karavaeva, I. R. Ivashkin, “Monotonizatsiya modifitsirovannoi skhemy s ermitovoi interpolyatsiei dlya chislennogo resheniya neodnorodnogo uravneniya perenosa s pogloscheniem”, Preprinty IPM im. M. V. Keldysha, 2024, 065, 40 pp.
E. N. Aristova, N. I. Karavaeva, “Realizatsiya bikompaktnoi skhemy dlya HOLO algoritma resheniya zadach perenosa izlucheniya v srede”, Preprinty IPM im. M. V. Keldysha, 2024, 064, 27 pp.
N. I. Karavaeva, “Bikompaktnye skhemy dlya resheniya odnogruppovoi sistemy uravnenii kvazidiffuzii sovmestno s uravneniem energii”, Preprinty IPM im. M. V. Keldysha, 2023, 025, 16 pp.
E. N. Aristova, N. I. Karavaeva, “Bikompaktnye skhemy dlya HOLO-algoritma resheniya uravneniya perenosa izlucheniya sovmestno s uravneniem energii”, Kompyuternye issledovaniya i modelirovanie, 15:6 (2023), 1429–1448
E. N. Aristova, G. O. Astafurov, “A third-order projection-characteristic method for solving the transport equation on unstructed grids”, Math. Models Comput. Simul., 16:2 (2024), 208–216
G. O. Astafurov, “Postroenie i issledovanie metoda CPP (Cubic Polynomial Projection) resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2022, 066, 56 pp.
E. N. Aristova, N. I. Karavaeva, “The bicompact schemes for numerical solving of Reed problem using HOLO algorithms”, Math. Models Comput. Simul., 14:2 (2022), 187–202
Elena N. Aristova, Smart Innovation, Systems and Technologies, 215, Smart Modelling for Engineering Systems, 2021, 51
E. N. Aristova, G. O. Astafurov, “Comparison of dissipation and dispersion properties of compact difference schemes for the numerical solution of the advection equation”, Comput. Math. Math. Phys., 61:11 (2021), 1711–1722
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.
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.
E. N. Aristova, N. I. Karavaeva, “The boundary conditions in the bicompact schemes for HOLO algorithms for solving the transport equation”, Math. Models Comput. Simul., 12:3 (2020), 271–281
B. V. Rogov, A. V. Chikitkin, “About the convergence and accuracy of the method of iterative approximate factorization of operators of multidimensional high-accuracy bicompact schemes”, Math. Models Comput. Simul., 12:5 (2020), 660–675
E. N. Aristova, N. I. Karavaeva, “Bikompaktnye skhemy vysokogo poryadka approksimatsii dlya uravnenii kvazidiffuzii”, Preprinty IPM im. M. V. Keldysha, 2018, 045, 28 pp.
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.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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