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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2016, Volume 158, Book 2, Pages 243–261
(Mi uzku1366)
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This article is cited in 8 scientific papers (total in 8 papers)
Numerical solution of the convective and diffusive transport problems in a heterogeneous porous medium using finite element method
M. V. Vasilyevaab, V. I. Vasilyeva, T. S. Timofeevaa a M. K. Ammosov North-Eastern Federal University, Yakutsk, 677000 Russia
b bInstitute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Abstract:
The finite element approximation of the convective and diffusive transport equation has been considered. Different methods for stabilization of the finite element approximation have been discussed: upwind approximation of the convective term using artificial diffusion (AD) and streamline upwind Petrov–Galerkin (SUPG) method, both used for stabilization of the classic Galerkin method. Another approach to approximation of the transport equation related to the discontinuous Galerkin method (DG) has been investigated. This method also allows to approximate the convective term using upwind schemes. The results of the numerical comparison of the considered schemes for the convective and diffusive transport problems in a porous media have been presented. The flow and transport in a highly contrast heterogeneous porous media that lead to the significant pressure gradients and, therefore, high velocities have been considered as test problems.
Keywords:
convection-diffusion equation, filtration, heterogeneous porous media, finite element method, numerical stabilization, classic Galerkin method, discontinuous Galerkin method.
Received: 23.03.2016
Citation:
M. V. Vasilyeva, V. I. Vasilyev, T. S. Timofeeva, “Numerical solution of the convective and diffusive transport problems in a heterogeneous porous medium using finite element method”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 158, no. 2, Kazan University, Kazan, 2016, 243–261
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https://www.mathnet.ru/eng/uzku1366 https://www.mathnet.ru/eng/uzku/v158/i2/p243
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