The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model
Abstract The viscous‐plastic sea ice model based on [2] describes the motion of sea ice for scales of several thousand kilometers. The numerical model for the simulation of sea ice circulation and evolution over a seasonal cycle includes the consideration of the sea ice thickness and sea ice concent...
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crwiley:10.1002/pamm.201900473 2024-06-02T08:14:12+00:00 The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model Nisters, Carina Schröder, Jörg Niekamp, Rainer Ricken, Tim 2019 http://dx.doi.org/10.1002/pamm.201900473 https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201900473 en eng Wiley http://creativecommons.org/licenses/by-nc-nd/4.0/ PAMM volume 19, issue 1 ISSN 1617-7061 1617-7061 journal-article 2019 crwiley https://doi.org/10.1002/pamm.201900473 2024-05-03T11:53:23Z Abstract The viscous‐plastic sea ice model based on [2] describes the motion of sea ice for scales of several thousand kilometers. The numerical model for the simulation of sea ice circulation and evolution over a seasonal cycle includes the consideration of the sea ice thickness and sea ice concentration. Transient advection equations describe the physical behavior of both thickness and concentration with the velocity of the sea ice as the coupling field. Recent research on a finite element implementation of the sea ice model is devoted to formulations based on the (mixed) Galerkin variational approach, compare to [1] and [6] for instance. Here, particular treatments are necessary regarding the stabilization of the complex numerical scheme, especially for the first‐order advection equation. It is therefore suggested to utilize the mixed least‐squares finite element method (LSFEM), which is well established in the branch of, e.g., fluid mechanics. A significant advantage of the method is its applicability to first‐order systems. Thus, this method results in stable and robust formulations also for not self‐adjoint operators like the tracer equations. Moreover, in [7], the authors provide a promising higher‐order time integration scheme for transient advection equations denoted as Taylor‐least‐squares scheme, which is investigated in this article. The presented least‐squares finite element formulation is based on the unsteady sea ice equations including two tracer equations of transient advection type. The numerical problem of a Box test case is investigated. Article in Journal/Newspaper Sea ice Wiley Online Library PAMM 19 1 |
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English |
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Abstract The viscous‐plastic sea ice model based on [2] describes the motion of sea ice for scales of several thousand kilometers. The numerical model for the simulation of sea ice circulation and evolution over a seasonal cycle includes the consideration of the sea ice thickness and sea ice concentration. Transient advection equations describe the physical behavior of both thickness and concentration with the velocity of the sea ice as the coupling field. Recent research on a finite element implementation of the sea ice model is devoted to formulations based on the (mixed) Galerkin variational approach, compare to [1] and [6] for instance. Here, particular treatments are necessary regarding the stabilization of the complex numerical scheme, especially for the first‐order advection equation. It is therefore suggested to utilize the mixed least‐squares finite element method (LSFEM), which is well established in the branch of, e.g., fluid mechanics. A significant advantage of the method is its applicability to first‐order systems. Thus, this method results in stable and robust formulations also for not self‐adjoint operators like the tracer equations. Moreover, in [7], the authors provide a promising higher‐order time integration scheme for transient advection equations denoted as Taylor‐least‐squares scheme, which is investigated in this article. The presented least‐squares finite element formulation is based on the unsteady sea ice equations including two tracer equations of transient advection type. The numerical problem of a Box test case is investigated. |
format |
Article in Journal/Newspaper |
author |
Nisters, Carina Schröder, Jörg Niekamp, Rainer Ricken, Tim |
spellingShingle |
Nisters, Carina Schröder, Jörg Niekamp, Rainer Ricken, Tim The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model |
author_facet |
Nisters, Carina Schröder, Jörg Niekamp, Rainer Ricken, Tim |
author_sort |
Nisters, Carina |
title |
The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model |
title_short |
The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model |
title_full |
The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model |
title_fullStr |
The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model |
title_full_unstemmed |
The Taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model |
title_sort |
taylor‐least‐squares time integrator scheme applied to tracer equations of a sea ice model |
publisher |
Wiley |
publishDate |
2019 |
url |
http://dx.doi.org/10.1002/pamm.201900473 https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201900473 |
genre |
Sea ice |
genre_facet |
Sea ice |
op_source |
PAMM volume 19, issue 1 ISSN 1617-7061 1617-7061 |
op_rights |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
op_doi |
https://doi.org/10.1002/pamm.201900473 |
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PAMM |
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19 |
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