Accurate and stable time stepping in ice sheet modeling
In this paper we introduce adaptive time step control for simulation of evolution of ice sheets. The discretization error in the approximations is estimated using "Milne's device" by comparing the result from two different methods in a predictor-corrector pair. Using a predictor-corre...
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ftdatacite:10.48550/arxiv.1605.06970 2023-05-15T16:40:33+02:00 Accurate and stable time stepping in ice sheet modeling Cheng, Gong Lötstedt, Per von Sydow, Lina 2016 https://dx.doi.org/10.48550/arxiv.1605.06970 https://arxiv.org/abs/1605.06970 unknown arXiv https://dx.doi.org/10.1016/j.jcp.2016.10.060 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Computational Physics physics.comp-ph FOS Physical sciences 65M99, 86-08, 86A40 article-journal Article ScholarlyArticle Text 2016 ftdatacite https://doi.org/10.48550/arxiv.1605.06970 https://doi.org/10.1016/j.jcp.2016.10.060 2022-04-01T11:40:58Z In this paper we introduce adaptive time step control for simulation of evolution of ice sheets. The discretization error in the approximations is estimated using "Milne's device" by comparing the result from two different methods in a predictor-corrector pair. Using a predictor-corrector pair the expensive part of the procedure, the solution of the velocity and pressure equations, is performed only once per time step and an estimate of the local error is easily obtained. The stability of the numerical solution is maintained and the accuracy is controlled by keeping the local error below a given threshold using PI-control. Depending on the threshold, the time step $Δt$ is bound by stability requirements or accuracy requirements. Our method takes a shorter $Δt$ than an implicit method but with less work in each time step and the solver is simpler. The method is analyzed theoretically with respect to stability and applied to the simulation of a 2D ice slab and a 3D circular ice sheet. %The automatically chosen $Δt$ is either restricted by accuracy or stability depedning on an error tolerance. The stability bounds in the experiments are explained by and agree well with the theoretical results. Text Ice Sheet DataCite Metadata Store (German National Library of Science and Technology) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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topic |
Computational Physics physics.comp-ph FOS Physical sciences 65M99, 86-08, 86A40 |
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Computational Physics physics.comp-ph FOS Physical sciences 65M99, 86-08, 86A40 Cheng, Gong Lötstedt, Per von Sydow, Lina Accurate and stable time stepping in ice sheet modeling |
topic_facet |
Computational Physics physics.comp-ph FOS Physical sciences 65M99, 86-08, 86A40 |
description |
In this paper we introduce adaptive time step control for simulation of evolution of ice sheets. The discretization error in the approximations is estimated using "Milne's device" by comparing the result from two different methods in a predictor-corrector pair. Using a predictor-corrector pair the expensive part of the procedure, the solution of the velocity and pressure equations, is performed only once per time step and an estimate of the local error is easily obtained. The stability of the numerical solution is maintained and the accuracy is controlled by keeping the local error below a given threshold using PI-control. Depending on the threshold, the time step $Δt$ is bound by stability requirements or accuracy requirements. Our method takes a shorter $Δt$ than an implicit method but with less work in each time step and the solver is simpler. The method is analyzed theoretically with respect to stability and applied to the simulation of a 2D ice slab and a 3D circular ice sheet. %The automatically chosen $Δt$ is either restricted by accuracy or stability depedning on an error tolerance. The stability bounds in the experiments are explained by and agree well with the theoretical results. |
format |
Text |
author |
Cheng, Gong Lötstedt, Per von Sydow, Lina |
author_facet |
Cheng, Gong Lötstedt, Per von Sydow, Lina |
author_sort |
Cheng, Gong |
title |
Accurate and stable time stepping in ice sheet modeling |
title_short |
Accurate and stable time stepping in ice sheet modeling |
title_full |
Accurate and stable time stepping in ice sheet modeling |
title_fullStr |
Accurate and stable time stepping in ice sheet modeling |
title_full_unstemmed |
Accurate and stable time stepping in ice sheet modeling |
title_sort |
accurate and stable time stepping in ice sheet modeling |
publisher |
arXiv |
publishDate |
2016 |
url |
https://dx.doi.org/10.48550/arxiv.1605.06970 https://arxiv.org/abs/1605.06970 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_relation |
https://dx.doi.org/10.1016/j.jcp.2016.10.060 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1605.06970 https://doi.org/10.1016/j.jcp.2016.10.060 |
_version_ |
1766030961201381376 |