Improved convergence and stability properties in a three-dimensional higher-order ice sheet model
We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force bala...
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ftdoajarticles:oai:doaj.org/article:b5353d9d1faf482aa5c39b40bfa94356 2023-05-15T16:40:35+02:00 Improved convergence and stability properties in a three-dimensional higher-order ice sheet model J. J. Fürst O. Rybak H. Goelzer B. De Smedt P. de Groen P. Huybrechts 2011-12-01T00:00:00Z https://doi.org/10.5194/gmd-4-1133-2011 https://doaj.org/article/b5353d9d1faf482aa5c39b40bfa94356 EN eng Copernicus Publications http://www.geosci-model-dev.net/4/1133/2011/gmd-4-1133-2011.pdf https://doaj.org/toc/1991-959X https://doaj.org/toc/1991-9603 doi:10.5194/gmd-4-1133-2011 1991-959X 1991-9603 https://doaj.org/article/b5353d9d1faf482aa5c39b40bfa94356 Geoscientific Model Development, Vol 4, Iss 4, Pp 1133-1149 (2011) Geology QE1-996.5 article 2011 ftdoajarticles https://doi.org/10.5194/gmd-4-1133-2011 2022-12-31T12:37:41Z We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented. Article in Journal/Newspaper Ice Sheet Directory of Open Access Journals: DOAJ Articles Geoscientific Model Development 4 4 1133 1149 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Geology QE1-996.5 |
spellingShingle |
Geology QE1-996.5 J. J. Fürst O. Rybak H. Goelzer B. De Smedt P. de Groen P. Huybrechts Improved convergence and stability properties in a three-dimensional higher-order ice sheet model |
topic_facet |
Geology QE1-996.5 |
description |
We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented. |
format |
Article in Journal/Newspaper |
author |
J. J. Fürst O. Rybak H. Goelzer B. De Smedt P. de Groen P. Huybrechts |
author_facet |
J. J. Fürst O. Rybak H. Goelzer B. De Smedt P. de Groen P. Huybrechts |
author_sort |
J. J. Fürst |
title |
Improved convergence and stability properties in a three-dimensional higher-order ice sheet model |
title_short |
Improved convergence and stability properties in a three-dimensional higher-order ice sheet model |
title_full |
Improved convergence and stability properties in a three-dimensional higher-order ice sheet model |
title_fullStr |
Improved convergence and stability properties in a three-dimensional higher-order ice sheet model |
title_full_unstemmed |
Improved convergence and stability properties in a three-dimensional higher-order ice sheet model |
title_sort |
improved convergence and stability properties in a three-dimensional higher-order ice sheet model |
publisher |
Copernicus Publications |
publishDate |
2011 |
url |
https://doi.org/10.5194/gmd-4-1133-2011 https://doaj.org/article/b5353d9d1faf482aa5c39b40bfa94356 |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Geoscientific Model Development, Vol 4, Iss 4, Pp 1133-1149 (2011) |
op_relation |
http://www.geosci-model-dev.net/4/1133/2011/gmd-4-1133-2011.pdf https://doaj.org/toc/1991-959X https://doaj.org/toc/1991-9603 doi:10.5194/gmd-4-1133-2011 1991-959X 1991-9603 https://doaj.org/article/b5353d9d1faf482aa5c39b40bfa94356 |
op_doi |
https://doi.org/10.5194/gmd-4-1133-2011 |
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Geoscientific Model Development |
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4 |
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4 |
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1133 |
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1149 |
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