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Matematicheskoe modelirovanie, 2016, Volume 28, Number 7, Pages 20–30 (Mi mm3745)  

This article is cited in 6 scientific papers (total in 6 papers)

The second order short-characteristics method for the solution of the transport equation on a tetrahedron grid

E. N. Aristovaab, G. O. Astafurova

a Keldysh Institute of Applied Mathematics RAS
b Moscow Institute Physics and Technology
Full-text PDF (311 kB) Citations (6)
References:
Abstract: In this paper the second order approximation method on unstructured tetrahedral mesh for solving the transport equation by the use of short characteristics is constructed. Second order polynomial interpolation constructed by the values at the tops of the illuminated face and the values of the integrals of the unknown function along the edges of the same face. The value in the nonilluminated top is obtained by integrating along the characteristic inside the tetrahedron from the interpolated value on the illuminated face. Accuracy of the method depends on the interpolation accuracy and the accuracy of the right part integration along the segment of the characteristic. In the case of piecewise constant approximation of the right part it is the second order of convergence on the condition that the solution has sufficient smoothness. On the test problems it is shown that in the case of smooth solutions the method has the order of convergence a little less than second, in the case of non-differentiable solution — lesser than first.
Keywords: transport equation, method of short characteristics, interpolation-characteristic method, second order of approximation.
Received: 09.02.2015
English version:
Mathematical Models and Computer Simulations, 2017, Volume 9, Issue 1, Pages 40–47
DOI: https://doi.org/10.1134/S2070048217010045
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. N. Aristova, G. O. Astafurov, “The second order short-characteristics method for the solution of the transport equation on a tetrahedron grid”, Mat. Model., 28:7 (2016), 20–30; Math. Models Comput. Simul., 9:1 (2017), 40–47
Citation in format AMSBIB
\Bibitem{AriAst16}
\by E.~N.~Aristova, G.~O.~Astafurov
\paper The second order short-characteristics method for the solution of the transport equation on a tetrahedron grid
\jour Mat. Model.
\yr 2016
\vol 28
\issue 7
\pages 20--30
\mathnet{http://mi.mathnet.ru/mm3745}
\elib{https://elibrary.ru/item.asp?id=26604113}
\transl
\jour Math. Models Comput. Simul.
\yr 2017
\vol 9
\issue 1
\pages 40--47
\crossref{https://doi.org/10.1134/S2070048217010045}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85011977200}
Linking options:
  • https://www.mathnet.ru/eng/mm3745
  • https://www.mathnet.ru/eng/mm/v28/i7/p20
  • This publication is cited in the following 6 articles:
    1. E. N. Aristova, G. O. Astafurov, “Vysokotochnaya skhema dlya uravneniya perenosa v zadache neitronnoi zaschity”, Preprinty IPM im. M. V. Keldysha, 2024, 013, 21 pp.  mathnet  crossref
    2. Olga V. Nikolaeva, Sergey A. Gaifulin, Leonid P. Bass, Denis V. Dmitriev, Alexandr A. Nikolaev, “Influence of the spatial grid type on the result of calculating the neutron fields in the nuclear power plant shielding”, NUCET, 9:2 (2023), 99  crossref
    3. 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  mathnet  crossref  crossref
    4. G. O. Astafurov, “Postroenie i issledovanie metoda CPP (Cubic Polynomial Projection) resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2022, 066, 56 pp.  mathnet  crossref
    5. E. N. Aristova, G. O. Astafurov, “Characteristics scheme for the transport equation solving on a tetrahedron grid with barycentrical interpolation”, Math. Models Comput. Simul., 11:3 (2019), 349–359  mathnet  crossref
    6. G. O. Astafurov, “Algoritm obkhoda yacheek v kharakteristicheskikh metodakh resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2018, 193, 24 pp.  mathnet  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:60
    First page:7
     
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