A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling
In ice sheet and glacier modelling, the Finite Element Method is rapidly gaining popularity. However, constructing and updating meshes for ice sheets and glaciers is a non-trivial and computationally demanding task due to their thin, irregular, and time dependent geometry. In this paper we introduce...
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Umeå universitet, Institutionen för matematik och matematisk statistik
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ftumeauniv:oai:DiVA.org:umu-182763 2023-10-09T21:52:24+02:00 A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling Ahlkrona, Josefin Elfverson, Daniel 2021 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-182763 https://doi.org/10.1016/j.jcpx.2021.100090 eng eng Umeå universitet, Institutionen för matematik och matematisk statistik Department of Mathematics, Stockholm University, Stockholm, Sweden; Swedish e-Science Research Centre (SeRC), Stockholm, Sweden , 2021, 11, Journal of Computational Physics: X, 2021, 11, http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-182763 doi:10.1016/j.jcpx.2021.100090 Scopus 2-s2.0-85104304308 info:eu-repo/semantics/openAccess CutFEM Free boundary problems Ice sheet modelling Non-Newtonian flow Sharp interface methods Unfitted finite element methods Computational Mathematics Beräkningsmatematik Article in journal info:eu-repo/semantics/article text 2021 ftumeauniv https://doi.org/10.1016/j.jcpx.2021.100090 2023-09-22T13:59:28Z In ice sheet and glacier modelling, the Finite Element Method is rapidly gaining popularity. However, constructing and updating meshes for ice sheets and glaciers is a non-trivial and computationally demanding task due to their thin, irregular, and time dependent geometry. In this paper we introduce a novel approach to ice dynamics computations based on the unfitted Finite Element Method CutFEM, which lets the domain boundary cut through elements. By employing CutFEM, complex meshing and remeshing is avoided as the glacier can be immersed in a simple background mesh without loss of accuracy. The ice is modelled as a non-Newtonian, shear-thinning fluid obeying the p-Stokes (full Stokes) equations with the ice atmosphere interface as a moving free surface. A Navier slip boundary condition applies at the glacier base allowing both bedrock and subglacial lakes to be represented. Within the CutFEM framework we develop a strategy for handling non-linear viscosities and thin domains and show how glacier deformation can be modelled using a level set function. In numerical experiments we show that the expected order of accuracy is achieved and that the method is robust with respect to penalty parameters. As an application we compute the velocity field of the Swiss mountain glacier Haut Glacier d'Arolla in 2D with and without an underlying subglacial lake, and simulate the glacier deformation from year 1930 to 1932, with and without surface accumulation and basal melt. Article in Journal/Newspaper Ice Sheet Umeå University: Publications (DiVA) Journal of Computational Physics: X 11 100090 |
institution |
Open Polar |
collection |
Umeå University: Publications (DiVA) |
op_collection_id |
ftumeauniv |
language |
English |
topic |
CutFEM Free boundary problems Ice sheet modelling Non-Newtonian flow Sharp interface methods Unfitted finite element methods Computational Mathematics Beräkningsmatematik |
spellingShingle |
CutFEM Free boundary problems Ice sheet modelling Non-Newtonian flow Sharp interface methods Unfitted finite element methods Computational Mathematics Beräkningsmatematik Ahlkrona, Josefin Elfverson, Daniel A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling |
topic_facet |
CutFEM Free boundary problems Ice sheet modelling Non-Newtonian flow Sharp interface methods Unfitted finite element methods Computational Mathematics Beräkningsmatematik |
description |
In ice sheet and glacier modelling, the Finite Element Method is rapidly gaining popularity. However, constructing and updating meshes for ice sheets and glaciers is a non-trivial and computationally demanding task due to their thin, irregular, and time dependent geometry. In this paper we introduce a novel approach to ice dynamics computations based on the unfitted Finite Element Method CutFEM, which lets the domain boundary cut through elements. By employing CutFEM, complex meshing and remeshing is avoided as the glacier can be immersed in a simple background mesh without loss of accuracy. The ice is modelled as a non-Newtonian, shear-thinning fluid obeying the p-Stokes (full Stokes) equations with the ice atmosphere interface as a moving free surface. A Navier slip boundary condition applies at the glacier base allowing both bedrock and subglacial lakes to be represented. Within the CutFEM framework we develop a strategy for handling non-linear viscosities and thin domains and show how glacier deformation can be modelled using a level set function. In numerical experiments we show that the expected order of accuracy is achieved and that the method is robust with respect to penalty parameters. As an application we compute the velocity field of the Swiss mountain glacier Haut Glacier d'Arolla in 2D with and without an underlying subglacial lake, and simulate the glacier deformation from year 1930 to 1932, with and without surface accumulation and basal melt. |
format |
Article in Journal/Newspaper |
author |
Ahlkrona, Josefin Elfverson, Daniel |
author_facet |
Ahlkrona, Josefin Elfverson, Daniel |
author_sort |
Ahlkrona, Josefin |
title |
A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling |
title_short |
A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling |
title_full |
A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling |
title_fullStr |
A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling |
title_full_unstemmed |
A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling |
title_sort |
cut finite element method for non-newtonian free surface flows in 2d : application to glacier modelling |
publisher |
Umeå universitet, Institutionen för matematik och matematisk statistik |
publishDate |
2021 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-182763 https://doi.org/10.1016/j.jcpx.2021.100090 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_relation |
, 2021, 11, Journal of Computational Physics: X, 2021, 11, http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-182763 doi:10.1016/j.jcpx.2021.100090 Scopus 2-s2.0-85104304308 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1016/j.jcpx.2021.100090 |
container_title |
Journal of Computational Physics: X |
container_volume |
11 |
container_start_page |
100090 |
_version_ |
1779315558058033152 |