Solving the problem of non-stationary filtration of substance by the discontinuous Galerkin method on unstructured grids
- Авторы: Zhalnin R.V.1, Ladonkina M.E.2, Masyagin V.F.1, Tishkin V.F.2
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Учреждения:
- Mordovia State University
- Institute of Applied Mathematics
- Выпуск: Том 56, № 6 (2016)
- Страницы: 977-986
- Раздел: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/178474
- DOI: https://doi.org/10.1134/S0965542516060245
- ID: 178474
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Аннотация
A numerical algorithm is proposed for solving the problem of non-stationary filtration of substance in anisotropic media by the Galerkin method with discontinuous basis functions on unstructured triangular grids. A characteristic feature of this method is that the flux variables are considered on the dual grid. The dual grid comprises median control volumes around the nodes of the original triangular grid. The flux values of the quantities on the boundary of an element are calculated with the help of stabilizing additions. For averaging the permeability tensor over the cells of the dual grid, the method of support operators is applied. The method is studied on the example of a two-dimensional boundary value problem. The convergence and approximation of the numerical method are analyzed, and results of mathematical modeling are presented. The numerical results demonstrate the applicability of this approach for solving problems of non-stationary filtration of substance in anisotropic media by the discontinuous Galerkin method on unstructured triangular grids.
Об авторах
R. Zhalnin
Mordovia State University
Автор, ответственный за переписку.
Email: zhalnin@gmail.com
Россия, ul. Bol’shevistskaya 68, Saransk, 430005
M. Ladonkina
Institute of Applied Mathematics
Email: zhalnin@gmail.com
Россия, Miusskaya pl. 4, Moscow, 125047
V. Masyagin
Mordovia State University
Email: zhalnin@gmail.com
Россия, ul. Bol’shevistskaya 68, Saransk, 430005
V. Tishkin
Institute of Applied Mathematics
Email: zhalnin@gmail.com
Россия, Miusskaya pl. 4, Moscow, 125047
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