Journal
MATHEMATICS
Volume 9, Issue 20, Pages -Publisher
MDPI
DOI: 10.3390/math9202545
Keywords
cryolithozone; heat and mass transfer; finite element methed; GMsFEM
Categories
Funding
- RSCF [20-71-00133]
- Ministry of science and higher education of the Russian Federation [N075-02-2020-1542/1]
- Russian Federation Government [N14.Y26.31.0013]
- Russian Science Foundation [20-71-00133] Funding Source: Russian Science Foundation
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In this work, a multiscale simulation method based on GMsFEM is designed for numerical modeling of fluid seepage in porous media under permafrost conditions. The method includes designing coarse-grid spaces and special algorithms to solve the coupled Richards equation and Stefan problem with heterogeneities. Testing on two- and three-dimensional models, including a quasi-real geometry, demonstrates the efficiency and accuracy of the proposed method.
In this work, we design a multiscale simulation method based on the Generalized Multiscale Finite Element Method (GMsFEM) for numerical modeling of fluid seepage under permafrost condition in heterogeneous soils. The complex multiphysical model consists of the coupled Richards equation and the Stefan problem. These problems often contain heterogeneities due to variations of soil properties. For this reason, we design coarse-grid spaces for the multiphysical problem and design special algorithms for solving the overall problem. A numerical method has been tested on two- and three-dimensional model problems. A a quasi-real geometry with a complex surface is considered for the three-dimensional case. We demonstrate the efficiency and accuracy of the proposed method using several representative numerical results.
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