E. N. Aristova, B. V. Rogov, “About implementation of boundary conditions in the bicompact schemes for a linear transport equation”, Mat. Model., 24:10 (2012), 3–14; Math. Models Comput. Simul., 5:3 (2013), 199

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Matematicheskoe modelirovanie, 2012, Volume 24, Number 10, Pages 3–14 (Mi mm3316)

This article is cited in 22 scientific papers (total in 22 papers)

About implementation of boundary conditions in the bicompact schemes for a linear transport equation

E. N. Aristova^ab, B. V. Rogov^ab

^a Keldysh Institute of Applied Mathematics of RAS, Moscow
^b Moscow Institute of Physics and Technology, State University

Full-text PDF (421 kB) Citations (22)

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Abstract: The question of the boundary conditions implementation in the previously proposed bicompact schemes is investigated for the linear transfer equation. These schemes are constructed by the method of lines, they are conservative, monotonic and economical, and can be solved by running method. To ensure a high accuracy of the bicompact schemes, the various ways of implementing boundary conditions are proposed. These schemes are based on the $A$-and $L$-stable diagonally implicit Runge–Kutta of third-order approximation for the integration of the transfer equation in time.

Keywords: linear transport equation, bicompact difference schemes, diagonally implicit Runge–Kutta schemes.

Received: 26.09.2011

English version:
Mathematical Models and Computer Simulations, 2013, Volume 5, Issue 3, Pages 199–207
DOI: https://doi.org/10.1134/S2070048213030022

Bibliographic databases:

Document Type: Article

UDC: 519.6

Language: Russian

Citation: E. N. Aristova, B. V. Rogov, “About implementation of boundary conditions in the bicompact schemes for a linear transport equation”, Mat. Model., 24:10 (2012), 3–14; Math. Models Comput. Simul., 5:3 (2013), 199–207

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mm3316

https://www.mathnet.ru/eng/mm/v24/i10/p3

This publication is cited in the following 22 articles:

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
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.
E. N. Aristova, M. I. Stoynov, “Bicompact schemes of solving an stationary transport equation by quasi–diffusion method”, Math. Models Comput. Simul., 8:6 (2016), 615–624
E. N. Aristova, B. V. Rogov, A. V. Chikitkin, “Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation”, Comput. Math. Math. Phys., 56:6 (2016), 962–976
A. V. Chikitkin, B. V. Rogov, E. N. Aristova, “High-order accurate bicompact schemes for solving the multidimensional inhomogeneous transport equation and their efficient parallel implementation”, Dokl. Math., 94:2 (2016), 517
E. N. Aristova, B. V. Rogov, A. V. Chikitkin, “Monotonization of high accuracy bicompact scheme for stationary multidimensional transport equation”, Math. Models Comput. Simul., 8:2 (2016), 108–117
A. A. Lyupa, D. N. Morozov, M. A. Trapeznikova, B. N. Chetverushkin, N. G. Churbanova, S. V. Lemeshevsky, “Simulation of oil recovery processes with the employment of high-performance computer systems”, Math. Models Comput. Simul., 8:2 (2016), 129–134
Aristova E.N., Rogov B.V., “Bicompact Scheme For the Multidimensional Stationary Linear Transport Equation”, Appl. Numer. Math., 93:SI (2015), 3–14
M. D. Bragin, B. V. Rogov, “Uniqueness of a high-order accurate bicompact scheme for quasilinear hyperbolic equations”, Comput. Math. Math. Phys., 54:5 (2014), 831–836
E. N. Aristova, D. F. Baydin, B. V. Rogov, “Bicompact scheme for linear inhomogeneous transport equation”, Math. Models Comput. Simul., 5:6 (2013), 586–594

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

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