A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms
In this short note, we discuss variational multiscale methods for solving porous media flows in high-contrast heterogeneous media with rough source terms. Our objective is to separate, as much as possible, subgrid effects induced by the media properties from those due to heterogeneous source terms....
| Main Authors: | , , |
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| Format: | Journal Article |
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Elsevier
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/51487 |
| _version_ | 1848758709800402944 |
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| author | Calo, Victor Efendiev, Y. Galvis, J. |
| author_facet | Calo, Victor Efendiev, Y. Galvis, J. |
| author_sort | Calo, Victor |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this short note, we discuss variational multiscale methods for solving porous media flows in high-contrast heterogeneous media with rough source terms. Our objective is to separate, as much as possible, subgrid effects induced by the media properties from those due to heterogeneous source terms. For this reason, enriched coarse spaces designed for high-contrast multiscale problems are used to represent the effects of heterogeneities of the media. Furthermore, rough source terms are captured via auxiliary correction equations that appear in the formulation of variational multiscale methods [23]. These auxiliary equations are localized and one can use additive or multiplicative constructions for the subgrid corrections as discussed in the current paper. Our preliminary numerical results show that one can capture the effects due to both spatial heterogeneities in the coefficients (such as permeability field) and source terms (e.g., due to singular well terms) in one iteration. We test the cases for both smooth source terms and rough source terms and show that with the multiplicative correction, the numerical approximations are more accurate compared to the additive correction. © 2010 Elsevier Ltd. |
| first_indexed | 2025-11-14T09:48:18Z |
| format | Journal Article |
| id | curtin-20.500.11937-51487 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:18Z |
| publishDate | 2011 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-514872017-09-13T15:35:59Z A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms Calo, Victor Efendiev, Y. Galvis, J. In this short note, we discuss variational multiscale methods for solving porous media flows in high-contrast heterogeneous media with rough source terms. Our objective is to separate, as much as possible, subgrid effects induced by the media properties from those due to heterogeneous source terms. For this reason, enriched coarse spaces designed for high-contrast multiscale problems are used to represent the effects of heterogeneities of the media. Furthermore, rough source terms are captured via auxiliary correction equations that appear in the formulation of variational multiscale methods [23]. These auxiliary equations are localized and one can use additive or multiplicative constructions for the subgrid corrections as discussed in the current paper. Our preliminary numerical results show that one can capture the effects due to both spatial heterogeneities in the coefficients (such as permeability field) and source terms (e.g., due to singular well terms) in one iteration. We test the cases for both smooth source terms and rough source terms and show that with the multiplicative correction, the numerical approximations are more accurate compared to the additive correction. © 2010 Elsevier Ltd. 2011 Journal Article http://hdl.handle.net/20.500.11937/51487 10.1016/j.advwatres.2010.12.011 Elsevier restricted |
| spellingShingle | Calo, Victor Efendiev, Y. Galvis, J. A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms |
| title | A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms |
| title_full | A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms |
| title_fullStr | A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms |
| title_full_unstemmed | A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms |
| title_short | A note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms |
| title_sort | note on variational multiscale methods for high-contrast heterogeneous porous media flows with rough source terms |
| url | http://hdl.handle.net/20.500.11937/51487 |