Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes
Abstract In this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demons...
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| Format: | Article |
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Wiley
2023-07-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2023WR034894 |
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| author | Kyle Pietrzyk Ilenia Battiato |
| author_facet | Kyle Pietrzyk Ilenia Battiato |
| author_sort | Kyle Pietrzyk |
| collection | DOAJ |
| description | Abstract In this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demonstrated in Part 1 where upscaled models are rigorously derived in moderately reactive physical regimes. After encoding the algorithm into Symbolica, an automated upscaling framework, we upscale two reactive mass transport problems and numerically validate the resulting nonlinear homogenized models by showing the absolute error estimates predicted by homogenization theory are satisfied. In both problems, nontrivial closure forms and closure problems are automatically formulated using the encoded strategy with no human interaction, nor prior knowledge regarding the closure required for the systems. We hope these demonstrations spark further interest in automated analytical frameworks for multiscale modeling, as such capabilities are invaluable for generating rigorous multiscale models of complex phenomena in porous media. |
| format | Article |
| id | doaj-art-253b16336f5e4ebeb5f6c485c44b94e2 |
| institution | Matheson Library |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-253b16336f5e4ebeb5f6c485c44b94e22025-07-04T06:40:25ZengWileyWater Resources Research0043-13971944-79732023-07-01597n/an/a10.1029/2023WR034894Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability RegimesKyle Pietrzyk0Ilenia Battiato1Department of Energy Resources Engineering Stanford University Stanford CA USADepartment of Energy Resources Engineering Stanford University Stanford CA USAAbstract In this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demonstrated in Part 1 where upscaled models are rigorously derived in moderately reactive physical regimes. After encoding the algorithm into Symbolica, an automated upscaling framework, we upscale two reactive mass transport problems and numerically validate the resulting nonlinear homogenized models by showing the absolute error estimates predicted by homogenization theory are satisfied. In both problems, nontrivial closure forms and closure problems are automatically formulated using the encoded strategy with no human interaction, nor prior knowledge regarding the closure required for the systems. We hope these demonstrations spark further interest in automated analytical frameworks for multiscale modeling, as such capabilities are invaluable for generating rigorous multiscale models of complex phenomena in porous media.https://doi.org/10.1029/2023WR034894symbolic upscalinghomogenizationreactive transport |
| spellingShingle | Kyle Pietrzyk Ilenia Battiato Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes Water Resources Research symbolic upscaling homogenization reactive transport |
| title | Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes |
| title_full | Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes |
| title_fullStr | Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes |
| title_full_unstemmed | Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes |
| title_short | Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes |
| title_sort | automated symbolic upscaling 2 model generation for extended applicability regimes |
| topic | symbolic upscaling homogenization reactive transport |
| url | https://doi.org/10.1029/2023WR034894 |
| work_keys_str_mv | AT kylepietrzyk automatedsymbolicupscaling2modelgenerationforextendedapplicabilityregimes AT ileniabattiato automatedsymbolicupscaling2modelgenerationforextendedapplicabilityregimes |