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...
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ftdoajarticles:oai:doaj.org/article:442622419e56465f978f23e45a92ba04 2023-05-15T16:40:18+02:00 Manufactured analytical solutions for isothermal full-Stokes ice sheet models A. Sargent J. L. Fastook 2010-08-01T00:00:00Z https://doi.org/10.5194/tc-4-285-2010 https://doaj.org/article/442622419e56465f978f23e45a92ba04 EN eng Copernicus Publications http://www.the-cryosphere.net/4/285/2010/tc-4-285-2010.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-4-285-2010 1994-0416 1994-0424 https://doaj.org/article/442622419e56465f978f23e45a92ba04 The Cryosphere, Vol 4, Iss 3, Pp 285-311 (2010) Environmental sciences GE1-350 Geology QE1-996.5 article 2010 ftdoajarticles https://doi.org/10.5194/tc-4-285-2010 2022-12-30T23:37:29Z 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 Directory of Open Access Journals: DOAJ Articles The Cryosphere 4 3 285 311 |
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 A. Sargent J. L. Fastook Manufactured analytical solutions for isothermal full-Stokes ice sheet models |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
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 |
A. Sargent J. L. Fastook |
author_facet |
A. Sargent J. L. Fastook |
author_sort |
A. Sargent |
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://doaj.org/article/442622419e56465f978f23e45a92ba04 |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_source |
The Cryosphere, Vol 4, Iss 3, Pp 285-311 (2010) |
op_relation |
http://www.the-cryosphere.net/4/285/2010/tc-4-285-2010.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-4-285-2010 1994-0416 1994-0424 https://doaj.org/article/442622419e56465f978f23e45a92ba04 |
op_doi |
https://doi.org/10.5194/tc-4-285-2010 |
container_title |
The Cryosphere |
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4 |
container_issue |
3 |
container_start_page |
285 |
op_container_end_page |
311 |
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1766030680974688256 |