Two-scale convergence of a model for flow in a partially fissured medium
The distributed-microstructure model for the flow of single phase fluid in a partially fissured composite medium due to Douglas-Peszynska-Showalter [12] is extended to a quasi-linear version. This model contains the geometry of the local cells distributed throughout the medium, the flux exchange acr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
1999-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1999/02/abstr.html |
| _version_ | 1818273408716111872 |
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| author | G. W. Clark Ralph E. Showalter |
| author_facet | G. W. Clark Ralph E. Showalter |
| author_sort | G. W. Clark |
| collection | DOAJ |
| description | The distributed-microstructure model for the flow of single phase fluid in a partially fissured composite medium due to Douglas-Peszynska-Showalter [12] is extended to a quasi-linear version. This model contains the geometry of the local cells distributed throughout the medium, the flux exchange across their intricate interface with the imbedded fissure system, and the secondary flux resulting from diffusion paths within the matrix. Both the exact but highly singular micro-model and the macro-model are shown to be well-posed, and it is proved that the solution of the micro-model is two-scale convergent to that of the macro-model as the spatial parameter goes to zero. In the linear case, the effective coefficients are obtained by a partial decoupling of the homogenized system. |
| first_indexed | 2024-12-12T21:57:30Z |
| format | Article |
| id | doaj.art-96b8e47077524e718b65606930859e59 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T21:57:30Z |
| publishDate | 1999-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-96b8e47077524e718b65606930859e592022-12-22T00:10:35ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911999-01-01199902120Two-scale convergence of a model for flow in a partially fissured mediumG. W. ClarkRalph E. ShowalterThe distributed-microstructure model for the flow of single phase fluid in a partially fissured composite medium due to Douglas-Peszynska-Showalter [12] is extended to a quasi-linear version. This model contains the geometry of the local cells distributed throughout the medium, the flux exchange across their intricate interface with the imbedded fissure system, and the secondary flux resulting from diffusion paths within the matrix. Both the exact but highly singular micro-model and the macro-model are shown to be well-posed, and it is proved that the solution of the micro-model is two-scale convergent to that of the macro-model as the spatial parameter goes to zero. In the linear case, the effective coefficients are obtained by a partial decoupling of the homogenized system.http://ejde.math.txstate.edu/Volumes/1999/02/abstr.htmlfissured mediumhomogenizationtwo-scale convergencedual permeabilitymodelingmicrostructure |
| spellingShingle | G. W. Clark Ralph E. Showalter Two-scale convergence of a model for flow in a partially fissured medium Electronic Journal of Differential Equations fissured medium homogenization two-scale convergence dual permeability modeling microstructure |
| title | Two-scale convergence of a model for flow in a partially fissured medium |
| title_full | Two-scale convergence of a model for flow in a partially fissured medium |
| title_fullStr | Two-scale convergence of a model for flow in a partially fissured medium |
| title_full_unstemmed | Two-scale convergence of a model for flow in a partially fissured medium |
| title_short | Two-scale convergence of a model for flow in a partially fissured medium |
| title_sort | two scale convergence of a model for flow in a partially fissured medium |
| topic | fissured medium homogenization two-scale convergence dual permeability modeling microstructure |
| url | http://ejde.math.txstate.edu/Volumes/1999/02/abstr.html |
| work_keys_str_mv | AT gwclark twoscaleconvergenceofamodelforflowinapartiallyfissuredmedium AT ralpheshowalter twoscaleconvergenceofamodelforflowinapartiallyfissuredmedium |