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.
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
\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}
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https://www.mathnet.ru/eng/mm3745
https://www.mathnet.ru/eng/mm/v28/i7/p20
This publication is cited in the following 6 articles:
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.
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
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, 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
G. O. Astafurov, “Algoritm obkhoda yacheek v kharakteristicheskikh metodakh resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2018, 193, 24 pp.
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