Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models
The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for the three-dimensional, isothermal, nonlinear Stokes model for flows in glaciers and ice sheets. The solution construction procedure starts w...
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ftdoajarticles:oai:doaj.org/article:9a63418174a541bf9aa31f0916f3d5cb 2023-05-15T16:40:09+02:00 Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models W. Leng L. Ju M. Gunzburger S. Price 2013-01-01T00:00:00Z https://doi.org/10.5194/tc-7-19-2013 https://doaj.org/article/9a63418174a541bf9aa31f0916f3d5cb EN eng Copernicus Publications http://www.the-cryosphere.net/7/19/2013/tc-7-19-2013.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-7-19-2013 1994-0416 1994-0424 https://doaj.org/article/9a63418174a541bf9aa31f0916f3d5cb The Cryosphere, Vol 7, Iss 1, Pp 19-29 (2013) Environmental sciences GE1-350 Geology QE1-996.5 article 2013 ftdoajarticles https://doi.org/10.5194/tc-7-19-2013 2022-12-31T12:35:09Z The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for the three-dimensional, isothermal, nonlinear Stokes model for flows in glaciers and ice sheets. The solution construction procedure starts with kinematic boundary conditions and is mainly based on the solution of a first-order partial differential equation for the ice velocity that satisfies the incompressibility condition. The manufactured solutions depend on the geometry of the ice sheet, basal sliding parameters, and ice softness. Initial conditions are taken from the periodic geometry of a standard problem of the ISMIP-HOM benchmark tests. The upper surface is altered through the manufactured solution procedure to generate an analytic solution for the time-dependent flow problem. We then use this manufactured solution to verify a parallel, high-order accurate, finite element Stokes ice-sheet model. Simulation results from the computational model show good convergence to the manufactured analytic solution. Article in Journal/Newspaper Ice Sheet The Cryosphere Directory of Open Access Journals: DOAJ Articles The Cryosphere 7 1 19 29 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Environmental sciences GE1-350 Geology QE1-996.5 |
spellingShingle |
Environmental sciences GE1-350 Geology QE1-996.5 W. Leng L. Ju M. Gunzburger S. Price Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
description |
The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for the three-dimensional, isothermal, nonlinear Stokes model for flows in glaciers and ice sheets. The solution construction procedure starts with kinematic boundary conditions and is mainly based on the solution of a first-order partial differential equation for the ice velocity that satisfies the incompressibility condition. The manufactured solutions depend on the geometry of the ice sheet, basal sliding parameters, and ice softness. Initial conditions are taken from the periodic geometry of a standard problem of the ISMIP-HOM benchmark tests. The upper surface is altered through the manufactured solution procedure to generate an analytic solution for the time-dependent flow problem. We then use this manufactured solution to verify a parallel, high-order accurate, finite element Stokes ice-sheet model. Simulation results from the computational model show good convergence to the manufactured analytic solution. |
format |
Article in Journal/Newspaper |
author |
W. Leng L. Ju M. Gunzburger S. Price |
author_facet |
W. Leng L. Ju M. Gunzburger S. Price |
author_sort |
W. Leng |
title |
Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models |
title_short |
Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models |
title_full |
Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models |
title_fullStr |
Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models |
title_full_unstemmed |
Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models |
title_sort |
manufactured solutions and the verification of three-dimensional stokes ice-sheet models |
publisher |
Copernicus Publications |
publishDate |
2013 |
url |
https://doi.org/10.5194/tc-7-19-2013 https://doaj.org/article/9a63418174a541bf9aa31f0916f3d5cb |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_source |
The Cryosphere, Vol 7, Iss 1, Pp 19-29 (2013) |
op_relation |
http://www.the-cryosphere.net/7/19/2013/tc-7-19-2013.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-7-19-2013 1994-0416 1994-0424 https://doaj.org/article/9a63418174a541bf9aa31f0916f3d5cb |
op_doi |
https://doi.org/10.5194/tc-7-19-2013 |
container_title |
The Cryosphere |
container_volume |
7 |
container_issue |
1 |
container_start_page |
19 |
op_container_end_page |
29 |
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1766030536855257088 |