Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model
Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/938727 |
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| _version_ | 1841524869334827008 |
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| author | Viviane Klein Malgorzata Peszynska |
| author_facet | Viviane Klein Malgorzata Peszynska |
| author_sort | Viviane Klein |
| collection | DOAJ |
| description | Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model. Our numerical results show that the micro-model solutions appear to converge to the macro-model linearly with the parameter ε of periodic geometry. For the two-grid discretization, the a priori and a posteriori error estimates are proved, and we show how to adapt the grid for each component independently. |
| format | Article |
| id | doaj-art-7711e9c0776c4cf59b98b0971bab4703 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7711e9c0776c4cf59b98b0971bab47032025-02-03T05:47:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/938727938727Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-ModelViviane Klein0Malgorzata Peszynska1Campus Araranguá, Universidade Federal de Santa Catarina, Rua Pedro João Pereira, 150, 88900-000 Araranguá, SC, BrazilDepartment of Mathematics, Oregon State University, 368 Kidder Hall, Corvallis, Oregon 97331-4605, USADouble-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model. Our numerical results show that the micro-model solutions appear to converge to the macro-model linearly with the parameter ε of periodic geometry. For the two-grid discretization, the a priori and a posteriori error estimates are proved, and we show how to adapt the grid for each component independently.http://dx.doi.org/10.1155/2012/938727 |
| spellingShingle | Viviane Klein Malgorzata Peszynska Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model Journal of Applied Mathematics |
| title | Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model |
| title_full | Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model |
| title_fullStr | Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model |
| title_full_unstemmed | Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model |
| title_short | Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model |
| title_sort | adaptive double diffusion model and comparison to a highly heterogeneous micro model |
| url | http://dx.doi.org/10.1155/2012/938727 |
| work_keys_str_mv | AT vivianeklein adaptivedoublediffusionmodelandcomparisontoahighlyheterogeneousmicromodel AT malgorzatapeszynska adaptivedoublediffusionmodelandcomparisontoahighlyheterogeneousmicromodel |