Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice
The flow of glacial ice is typically approximated as a nonNewtonian viscous fluid, with the momentum balance described by (an approximation to) the Stokes equations, and the nonlinear rheology described by a flow law. The most commonly used rheological law for glacial ice, Glen's flow law, yiel...
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Cambridge University Press
2024-01-01
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| Series: | Journal of Glaciology |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S0022143024000455/type/journal_article |
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| author | Constantijn J. Berends Roderik S. W. van de Wal Paul A. Zegeling |
| author_facet | Constantijn J. Berends Roderik S. W. van de Wal Paul A. Zegeling |
| author_sort | Constantijn J. Berends |
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| description | The flow of glacial ice is typically approximated as a nonNewtonian viscous fluid, with the momentum balance described by (an approximation to) the Stokes equations, and the nonlinear rheology described by a flow law. The most commonly used rheological law for glacial ice, Glen's flow law, yields infinite viscosity in the case of zero deformation, which can be the case at the ice surface. This poses a problem when solving the momentum balance numerically. We show that two commonly-used discretisation schemes for the boundary conditions at the ice surface and base, which yield proper numerical convergence when applied to simpler problems, produce poor numerical convergence and large errors, when used to solve the momentum balance with Glen's flow law. We show that a discretisation scheme based on the concept of ghost nodes, which substitutes the boundary conditions directly into the momentum balance equations, yields second-order numerical convergence and errors that can be up to four orders of magnitude smaller. These results are robust across different momentum balance approximations. We show that the improved boundary conditions are particularly useful for solving the 3-D higher-order Blatter-Pattyn Approximation (BPA). In general, this work underlines the importance of thoroughly verifying the numerical solvers used in ice-sheet models, before applying them to future projections of ice-sheet mass loss. |
| format | Article |
| id | doaj-art-687ce068548a448b9d431b28da52e1b4 |
| institution | Kabale University |
| issn | 0022-1430 1727-5652 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
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| series | Journal of Glaciology |
| spelling | doaj-art-687ce068548a448b9d431b28da52e1b42025-01-16T21:52:00ZengCambridge University PressJournal of Glaciology0022-14301727-56522024-01-017010.1017/jog.2024.45Improvements on the discretisation of boundary conditions to the momentum balance for glacial iceConstantijn J. Berends0https://orcid.org/0000-0002-2961-0350Roderik S. W. van de Wal1https://orcid.org/0000-0003-2543-3892Paul A. Zegeling2Institute for Marine and Atmospheric research Utrecht (IMAU), Utrecht University, Utrecht, The NetherlandsInstitute for Marine and Atmospheric research Utrecht (IMAU), Utrecht University, Utrecht, The Netherlands Faculty of Geosciences, Department of Physical Geography, Utrecht University, Utrecht, The NetherlandsFaculty of Science, Department of Mathematics, Utrecht University, Utrecht, The NetherlandsThe flow of glacial ice is typically approximated as a nonNewtonian viscous fluid, with the momentum balance described by (an approximation to) the Stokes equations, and the nonlinear rheology described by a flow law. The most commonly used rheological law for glacial ice, Glen's flow law, yields infinite viscosity in the case of zero deformation, which can be the case at the ice surface. This poses a problem when solving the momentum balance numerically. We show that two commonly-used discretisation schemes for the boundary conditions at the ice surface and base, which yield proper numerical convergence when applied to simpler problems, produce poor numerical convergence and large errors, when used to solve the momentum balance with Glen's flow law. We show that a discretisation scheme based on the concept of ghost nodes, which substitutes the boundary conditions directly into the momentum balance equations, yields second-order numerical convergence and errors that can be up to four orders of magnitude smaller. These results are robust across different momentum balance approximations. We show that the improved boundary conditions are particularly useful for solving the 3-D higher-order Blatter-Pattyn Approximation (BPA). In general, this work underlines the importance of thoroughly verifying the numerical solvers used in ice-sheet models, before applying them to future projections of ice-sheet mass loss.https://www.cambridge.org/core/product/identifier/S0022143024000455/type/journal_articleGlacial rheologyice dynamicsice-sheet modelling |
| spellingShingle | Constantijn J. Berends Roderik S. W. van de Wal Paul A. Zegeling Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice Journal of Glaciology Glacial rheology ice dynamics ice-sheet modelling |
| title | Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice |
| title_full | Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice |
| title_fullStr | Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice |
| title_full_unstemmed | Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice |
| title_short | Improvements on the discretisation of boundary conditions to the momentum balance for glacial ice |
| title_sort | improvements on the discretisation of boundary conditions to the momentum balance for glacial ice |
| topic | Glacial rheology ice dynamics ice-sheet modelling |
| url | https://www.cambridge.org/core/product/identifier/S0022143024000455/type/journal_article |
| work_keys_str_mv | AT constantijnjberends improvementsonthediscretisationofboundaryconditionstothemomentumbalanceforglacialice AT roderikswvandewal improvementsonthediscretisationofboundaryconditionstothemomentumbalanceforglacialice AT paulazegeling improvementsonthediscretisationofboundaryconditionstothemomentumbalanceforglacialice |