Manufactured analytical solutions for isothermal full-Stokes ice sheet models
We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construc...
Published in: | The Cryosphere |
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Copernicus Publications
2010
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ftnonlinearchiv:oai:noa.gwlb.de:cop_mods_00028625 2023-05-15T16:40:17+02:00 Manufactured analytical solutions for isothermal full-Stokes ice sheet models Sargent, A. Fastook, J. L. 2010-08 electronic https://doi.org/10.5194/tc-4-285-2010 https://noa.gwlb.de/receive/cop_mods_00028625 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00028580/tc-4-285-2010.pdf https://tc.copernicus.org/articles/4/285/2010/tc-4-285-2010.pdf eng eng Copernicus Publications The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-4-285-2010 https://noa.gwlb.de/receive/cop_mods_00028625 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00028580/tc-4-285-2010.pdf https://tc.copernicus.org/articles/4/285/2010/tc-4-285-2010.pdf uneingeschränkt info:eu-repo/semantics/openAccess article Verlagsveröffentlichung article Text doc-type:article 2010 ftnonlinearchiv https://doi.org/10.5194/tc-4-285-2010 2022-02-08T22:48:06Z We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions. Article in Journal/Newspaper Ice Sheet The Cryosphere Niedersächsisches Online-Archiv NOA The Cryosphere 4 3 285 311 |
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English |
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article Verlagsveröffentlichung |
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article Verlagsveröffentlichung Sargent, A. Fastook, J. L. Manufactured analytical solutions for isothermal full-Stokes ice sheet models |
topic_facet |
article Verlagsveröffentlichung |
description |
We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions. |
format |
Article in Journal/Newspaper |
author |
Sargent, A. Fastook, J. L. |
author_facet |
Sargent, A. Fastook, J. L. |
author_sort |
Sargent, A. |
title |
Manufactured analytical solutions for isothermal full-Stokes ice sheet models |
title_short |
Manufactured analytical solutions for isothermal full-Stokes ice sheet models |
title_full |
Manufactured analytical solutions for isothermal full-Stokes ice sheet models |
title_fullStr |
Manufactured analytical solutions for isothermal full-Stokes ice sheet models |
title_full_unstemmed |
Manufactured analytical solutions for isothermal full-Stokes ice sheet models |
title_sort |
manufactured analytical solutions for isothermal full-stokes ice sheet models |
publisher |
Copernicus Publications |
publishDate |
2010 |
url |
https://doi.org/10.5194/tc-4-285-2010 https://noa.gwlb.de/receive/cop_mods_00028625 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00028580/tc-4-285-2010.pdf https://tc.copernicus.org/articles/4/285/2010/tc-4-285-2010.pdf |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_relation |
The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-4-285-2010 https://noa.gwlb.de/receive/cop_mods_00028625 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00028580/tc-4-285-2010.pdf https://tc.copernicus.org/articles/4/285/2010/tc-4-285-2010.pdf |
op_rights |
uneingeschränkt info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.5194/tc-4-285-2010 |
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The Cryosphere |
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4 |
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285 |
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311 |
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1766030669769605120 |