Abstract:
The present paper is devoted to the construction of the (Cubic Polynomial Projection) method for solving the linear transport of neutral particles or unpolarized radiation on tetrahedra. The paper presents and proves estimates for the accuracy of the resulting numerical solution. The absorption coefficient is approximated by a constant value in the cell, the source is a second-degree polynomial in the cell, and the boundary condition is a third-degree polynomial on the faces. Under additional conditions, the method can reach the third order of convergence. The method is based on the characteristic properties of the transport equation, and in some sense, it is a generalization of the CIP
(cubic-Interpolation pseudo-particle) method based on Hermitian interpolation in tetrahedra. The success of the method is ensured by the use of projection operators for constructing the scheme instead of the interpolation ones.
Keywords:
transport equation, projective characteristic method, tetrahedra cells.
Document Type:
Preprint
Language: Russian
Citation:
G. O. Astafurov, “Construction and investigation of the CPP (Cubic Polynomial Projection) method for the transport equation solving”, Keldysh Institute preprints, 2022, 066, 56 pp.
\Bibitem{Ast22}
\by G.~O.~Astafurov
\paper Construction and investigation of the CPP (Cubic Polynomial Projection) method for the transport equation solving
\jour Keldysh Institute preprints
\yr 2022
\papernumber 066
\totalpages 56
\mathnet{http://mi.mathnet.ru/ipmp3091}
\crossref{https://doi.org/10.20948/prepr-2022-66}
Linking options:
https://www.mathnet.ru/eng/ipmp3091
https://www.mathnet.ru/eng/ipmp/y2022/p66
This publication is cited in the following 2 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.
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
Citation in format AMSBIB
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