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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ftdoajarticles:oai:doaj.org/article:2b17cc993c6f46aaa1ffd16f08f806f3 2023-05-15T16:40:40+02:00 A cut finite element method for non-Newtonian free surface flows in 2D - application to glacier modelling Josefin Ahlkrona Daniel Elfverson 2021-06-01T00:00:00Z https://doi.org/10.1016/j.jcpx.2021.100090 https://doaj.org/article/2b17cc993c6f46aaa1ffd16f08f806f3 EN eng Elsevier http://www.sciencedirect.com/science/article/pii/S259005522100007X https://doaj.org/toc/2590-0552 2590-0552 doi:10.1016/j.jcpx.2021.100090 https://doaj.org/article/2b17cc993c6f46aaa1ffd16f08f806f3 Journal of Computational Physics: X, Vol 11, Iss , Pp 100090- (2021) Ice sheet modelling CutFEM Free boundary problems Non-Newtonian flow Unfitted finite element methods Sharp interface methods Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 article 2021 ftdoajarticles https://doi.org/10.1016/j.jcpx.2021.100090 2022-12-31T06:35:23Z 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 Directory of Open Access Journals: DOAJ Articles Journal of Computational Physics: X 11 100090 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Ice sheet modelling CutFEM Free boundary problems Non-Newtonian flow Unfitted finite element methods Sharp interface methods Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 |
spellingShingle |
Ice sheet modelling CutFEM Free boundary problems Non-Newtonian flow Unfitted finite element methods Sharp interface methods Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Josefin Ahlkrona Daniel Elfverson A cut finite element method for non-Newtonian free surface flows in 2D - application to glacier modelling |
topic_facet |
Ice sheet modelling CutFEM Free boundary problems Non-Newtonian flow Unfitted finite element methods Sharp interface methods Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 |
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 |
Josefin Ahlkrona Daniel Elfverson |
author_facet |
Josefin Ahlkrona Daniel Elfverson |
author_sort |
Josefin Ahlkrona |
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 |
Elsevier |
publishDate |
2021 |
url |
https://doi.org/10.1016/j.jcpx.2021.100090 https://doaj.org/article/2b17cc993c6f46aaa1ffd16f08f806f3 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Journal of Computational Physics: X, Vol 11, Iss , Pp 100090- (2021) |
op_relation |
http://www.sciencedirect.com/science/article/pii/S259005522100007X https://doaj.org/toc/2590-0552 2590-0552 doi:10.1016/j.jcpx.2021.100090 https://doaj.org/article/2b17cc993c6f46aaa1ffd16f08f806f3 |
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 |
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1766031072891502592 |