Stable finite volume element schemes for the shallow-ice approximation
ABSTRACT The isothermal, non-sliding shallow-ice approximation, combined with mass conservation, is a fundamental model for ice-sheet and glacier flow. It determines the ice extent, geometry and velocity by the solution of a free-boundary problem. In this paper, the steady-state form of this problem...
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Cambridge University Press (CUP)
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crcambridgeupr:10.1017/jog.2015.3 2024-03-03T08:44:37+00:00 Stable finite volume element schemes for the shallow-ice approximation BUELER, ED 2016 http://dx.doi.org/10.1017/jog.2015.3 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143015000039 en eng Cambridge University Press (CUP) http://creativecommons.org/licenses/by/4.0/ Journal of Glaciology volume 62, issue 232, page 230-242 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 2016 crcambridgeupr https://doi.org/10.1017/jog.2015.3 2024-02-08T08:40:57Z ABSTRACT The isothermal, non-sliding shallow-ice approximation, combined with mass conservation, is a fundamental model for ice-sheet and glacier flow. It determines the ice extent, geometry and velocity by the solution of a free-boundary problem. In this paper, the steady-state form of this problem is solved directly, without time-stepping, thereby demonstrating a fully implicit scheme with no stability restrictions. The classical Mahaffy (1976) finite difference method is first reinterpreted as a ‘finite volume element’ scheme that has both an everywhere-defined approximate thickness function and an approximation of the conservation equation in flux integral form. From this reinterpretation an improved scheme is built by using better quadrature in the integral and upwinding on that part of the flux which is proportional to the bed gradient. The discrete equations are then solved by a parallel Newton scheme which respects the constraint that ice thickness is non-negative. The results show good accuracy on both flat-bed and bedrock-step exact solutions. The method is then applied at high resolution to model the steady-state geometry of the Greenland ice sheet, using only bedrock elevation and present-day surface mass balance as input data. Article in Journal/Newspaper glacier Greenland Ice Sheet Journal of Glaciology Cambridge University Press Greenland Journal of Glaciology 62 232 230 242 |
institution |
Open Polar |
collection |
Cambridge University Press |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Earth-Surface Processes |
spellingShingle |
Earth-Surface Processes BUELER, ED Stable finite volume element schemes for the shallow-ice approximation |
topic_facet |
Earth-Surface Processes |
description |
ABSTRACT The isothermal, non-sliding shallow-ice approximation, combined with mass conservation, is a fundamental model for ice-sheet and glacier flow. It determines the ice extent, geometry and velocity by the solution of a free-boundary problem. In this paper, the steady-state form of this problem is solved directly, without time-stepping, thereby demonstrating a fully implicit scheme with no stability restrictions. The classical Mahaffy (1976) finite difference method is first reinterpreted as a ‘finite volume element’ scheme that has both an everywhere-defined approximate thickness function and an approximation of the conservation equation in flux integral form. From this reinterpretation an improved scheme is built by using better quadrature in the integral and upwinding on that part of the flux which is proportional to the bed gradient. The discrete equations are then solved by a parallel Newton scheme which respects the constraint that ice thickness is non-negative. The results show good accuracy on both flat-bed and bedrock-step exact solutions. The method is then applied at high resolution to model the steady-state geometry of the Greenland ice sheet, using only bedrock elevation and present-day surface mass balance as input data. |
format |
Article in Journal/Newspaper |
author |
BUELER, ED |
author_facet |
BUELER, ED |
author_sort |
BUELER, ED |
title |
Stable finite volume element schemes for the shallow-ice approximation |
title_short |
Stable finite volume element schemes for the shallow-ice approximation |
title_full |
Stable finite volume element schemes for the shallow-ice approximation |
title_fullStr |
Stable finite volume element schemes for the shallow-ice approximation |
title_full_unstemmed |
Stable finite volume element schemes for the shallow-ice approximation |
title_sort |
stable finite volume element schemes for the shallow-ice approximation |
publisher |
Cambridge University Press (CUP) |
publishDate |
2016 |
url |
http://dx.doi.org/10.1017/jog.2015.3 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143015000039 |
geographic |
Greenland |
geographic_facet |
Greenland |
genre |
glacier Greenland Ice Sheet Journal of Glaciology |
genre_facet |
glacier Greenland Ice Sheet Journal of Glaciology |
op_source |
Journal of Glaciology volume 62, issue 232, page 230-242 ISSN 0022-1430 1727-5652 |
op_rights |
http://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.1017/jog.2015.3 |
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Journal of Glaciology |
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62 |
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232 |
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230 |
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242 |
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1792500103773159424 |