A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model
We propose a fully discrete method for the multiscale Richards’ equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM), a fully discrete scheme combined with a regularized proced...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/657816 |
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| author | Haitao Cao Tao Yu Xingye Yue |
| author_facet | Haitao Cao Tao Yu Xingye Yue |
| author_sort | Haitao Cao |
| collection | DOAJ |
| description | We propose a fully discrete method for the multiscale Richards’ equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM), a fully discrete scheme combined with a regularized procedure is proposed. Including the numerical integration, the discretization is given by C0 piecewise finite element in space and an implicit scheme in time. Error estimates between the numerical solution and the solution of homogenized problem are derived under the assumption that the permeability is periodic. Numerical experiments with periodic and random permeability are carried out for the van Genuchten-Mualem model of Richards’ equation to show the efficiency and accuracy of the proposed method. |
| format | Article |
| id | doaj-art-29f4cac2be6845e2830520760cedb72d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-29f4cac2be6845e2830520760cedb72d2025-02-03T05:46:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/657816657816A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem ModelHaitao Cao0Tao Yu1Xingye Yue2Department of Mathematics and Physics, Hohai University, Changzhou Campus, Changzhou 213022, ChinaDepartment of Mathematics, Jinggangshan University, Ji’an, Jiangxi 343009, ChinaDepartment of Mathematics, Soochow University, Suzhou, Jiangsu 215006, ChinaWe propose a fully discrete method for the multiscale Richards’ equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM), a fully discrete scheme combined with a regularized procedure is proposed. Including the numerical integration, the discretization is given by C0 piecewise finite element in space and an implicit scheme in time. Error estimates between the numerical solution and the solution of homogenized problem are derived under the assumption that the permeability is periodic. Numerical experiments with periodic and random permeability are carried out for the van Genuchten-Mualem model of Richards’ equation to show the efficiency and accuracy of the proposed method.http://dx.doi.org/10.1155/2014/657816 |
| spellingShingle | Haitao Cao Tao Yu Xingye Yue A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model Journal of Applied Mathematics |
| title | A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model |
| title_full | A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model |
| title_fullStr | A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model |
| title_full_unstemmed | A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model |
| title_short | A Completely Discrete Heterogeneous Multiscale Finite Element Method for Multiscale Richards’ Equation of van Genuchten-Mualem Model |
| title_sort | completely discrete heterogeneous multiscale finite element method for multiscale richards equation of van genuchten mualem model |
| url | http://dx.doi.org/10.1155/2014/657816 |
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