Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models
<p>Typically, in finite element groundwater models, fractures are represented by two-dimensional triangular or quadrilateral elements. When embedded in a three-dimensional space, the Jacobian matrix governing the transformation from the global three-dimensional space to the local two-dimension...
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Copernicus Publications
2025-06-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://hess.copernicus.org/articles/29/2697/2025/hess-29-2697-2025.pdf |
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| _version_ | 1849471299630399488 |
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| author | R. de Rooij |
| author_facet | R. de Rooij |
| author_sort | R. de Rooij |
| collection | DOAJ |
| description | <p>Typically, in finite element groundwater models, fractures are represented by two-dimensional triangular or quadrilateral elements. When embedded in a three-dimensional space, the Jacobian matrix governing the transformation from the global three-dimensional space to the local two-dimensional space is rectangular and thus not invertible. There exist different approaches to obtain a unique mapping from local to global space even though the Jacobian matrix is not invertible. These approaches are discussed in this study. It is illustrated that all approaches yield the same result and may be applied to curved elements. The mapping of anisotropic hydraulic conductivity tensors for possibly curved fracture elements is also discussed.</p> |
| format | Article |
| id | doaj-art-dbca2adfae474d02b19f17795913bbdf |
| institution | Kabale University |
| issn | 1027-5606 1607-7938 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj-art-dbca2adfae474d02b19f17795913bbdf2025-08-20T03:24:52ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382025-06-01292697270510.5194/hess-29-2697-2025Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater modelsR. de Rooij0Water Institute, University of Florida, 570 Weil Hall, P.O. Box 116601, Gainesville, FL 32611-6601, USA<p>Typically, in finite element groundwater models, fractures are represented by two-dimensional triangular or quadrilateral elements. When embedded in a three-dimensional space, the Jacobian matrix governing the transformation from the global three-dimensional space to the local two-dimensional space is rectangular and thus not invertible. There exist different approaches to obtain a unique mapping from local to global space even though the Jacobian matrix is not invertible. These approaches are discussed in this study. It is illustrated that all approaches yield the same result and may be applied to curved elements. The mapping of anisotropic hydraulic conductivity tensors for possibly curved fracture elements is also discussed.</p>https://hess.copernicus.org/articles/29/2697/2025/hess-29-2697-2025.pdf |
| spellingShingle | R. de Rooij Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models Hydrology and Earth System Sciences |
| title | Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models |
| title_full | Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models |
| title_fullStr | Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models |
| title_full_unstemmed | Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models |
| title_short | Technical note: Finite element formulations to map discrete fracture elements in three-dimensional groundwater models |
| title_sort | technical note finite element formulations to map discrete fracture elements in three dimensional groundwater models |
| url | https://hess.copernicus.org/articles/29/2697/2025/hess-29-2697-2025.pdf |
| work_keys_str_mv | AT rderooij technicalnotefiniteelementformulationstomapdiscretefractureelementsinthreedimensionalgroundwatermodels |