Reformulating the full-Stokes ice sheet model for a more efficient computational solution
The first-order or Blatter-Pattyn ice sheet model, in spite of its approximate nature, is an attractive alternative to the full Stokes model in many applications because of its reduced computational demands. In contrast, the unapproximated Stokes ice sheet model is more difficult to solve and comput...
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ftcopernicus:oai:publications.copernicus.org:tc11647 2023-05-15T16:40:10+02:00 Reformulating the full-Stokes ice sheet model for a more efficient computational solution Dukowicz, J. K. 2018-09-27 application/pdf https://doi.org/10.5194/tc-6-21-2012 https://tc.copernicus.org/articles/6/21/2012/ eng eng doi:10.5194/tc-6-21-2012 https://tc.copernicus.org/articles/6/21/2012/ eISSN: 1994-0424 Text 2018 ftcopernicus https://doi.org/10.5194/tc-6-21-2012 2020-07-20T16:25:55Z The first-order or Blatter-Pattyn ice sheet model, in spite of its approximate nature, is an attractive alternative to the full Stokes model in many applications because of its reduced computational demands. In contrast, the unapproximated Stokes ice sheet model is more difficult to solve and computationally more expensive. This is primarily due to the fact that the Stokes model is indefinite and involves all three velocity components, as well as the pressure, while the Blatter-Pattyn discrete model is positive-definite and involves just the horizontal velocity components. The Stokes model is indefinite because it arises from a constrained minimization principle where the pressure acts as a Lagrange multiplier to enforce incompressibility. To alleviate these problems we reformulate the full Stokes problem into an unconstrained, positive-definite minimization problem, similar to the Blatter-Pattyn model but without any of the approximations. This is accomplished by introducing a divergence-free velocity field that satisfies appropriate boundary conditions as a trial function in the variational formulation, thus dispensing with the need for a pressure. Such a velocity field is obtained by vertically integrating the continuity equation to give the vertical velocity as a function of the horizontal velocity components, as is in fact done in the Blatter-Pattyn model. This leads to a reduced system for just the horizontal velocity components, again just as in the Blatter-Pattyn model, but now without approximation. In the process we obtain a new, reformulated Stokes action principle as well as a novel set of Euler-Lagrange partial differential equations and boundary conditions. The model is also generalized from the common case of an ice sheet in contact with and sliding along the bed to other situations, such as to a floating ice shelf. These results are illustrated and validated using a simple but nontrivial Stokes flow problem involving a sliding ice sheet. Text Ice Sheet Ice Shelf Copernicus Publications: E-Journals Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) The Cryosphere 6 1 21 34 |
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Open Polar |
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Copernicus Publications: E-Journals |
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ftcopernicus |
language |
English |
description |
The first-order or Blatter-Pattyn ice sheet model, in spite of its approximate nature, is an attractive alternative to the full Stokes model in many applications because of its reduced computational demands. In contrast, the unapproximated Stokes ice sheet model is more difficult to solve and computationally more expensive. This is primarily due to the fact that the Stokes model is indefinite and involves all three velocity components, as well as the pressure, while the Blatter-Pattyn discrete model is positive-definite and involves just the horizontal velocity components. The Stokes model is indefinite because it arises from a constrained minimization principle where the pressure acts as a Lagrange multiplier to enforce incompressibility. To alleviate these problems we reformulate the full Stokes problem into an unconstrained, positive-definite minimization problem, similar to the Blatter-Pattyn model but without any of the approximations. This is accomplished by introducing a divergence-free velocity field that satisfies appropriate boundary conditions as a trial function in the variational formulation, thus dispensing with the need for a pressure. Such a velocity field is obtained by vertically integrating the continuity equation to give the vertical velocity as a function of the horizontal velocity components, as is in fact done in the Blatter-Pattyn model. This leads to a reduced system for just the horizontal velocity components, again just as in the Blatter-Pattyn model, but now without approximation. In the process we obtain a new, reformulated Stokes action principle as well as a novel set of Euler-Lagrange partial differential equations and boundary conditions. The model is also generalized from the common case of an ice sheet in contact with and sliding along the bed to other situations, such as to a floating ice shelf. These results are illustrated and validated using a simple but nontrivial Stokes flow problem involving a sliding ice sheet. |
format |
Text |
author |
Dukowicz, J. K. |
spellingShingle |
Dukowicz, J. K. Reformulating the full-Stokes ice sheet model for a more efficient computational solution |
author_facet |
Dukowicz, J. K. |
author_sort |
Dukowicz, J. K. |
title |
Reformulating the full-Stokes ice sheet model for a more efficient computational solution |
title_short |
Reformulating the full-Stokes ice sheet model for a more efficient computational solution |
title_full |
Reformulating the full-Stokes ice sheet model for a more efficient computational solution |
title_fullStr |
Reformulating the full-Stokes ice sheet model for a more efficient computational solution |
title_full_unstemmed |
Reformulating the full-Stokes ice sheet model for a more efficient computational solution |
title_sort |
reformulating the full-stokes ice sheet model for a more efficient computational solution |
publishDate |
2018 |
url |
https://doi.org/10.5194/tc-6-21-2012 https://tc.copernicus.org/articles/6/21/2012/ |
long_lat |
ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
geographic |
Lagrange |
geographic_facet |
Lagrange |
genre |
Ice Sheet Ice Shelf |
genre_facet |
Ice Sheet Ice Shelf |
op_source |
eISSN: 1994-0424 |
op_relation |
doi:10.5194/tc-6-21-2012 https://tc.copernicus.org/articles/6/21/2012/ |
op_doi |
https://doi.org/10.5194/tc-6-21-2012 |
container_title |
The Cryosphere |
container_volume |
6 |
container_issue |
1 |
container_start_page |
21 |
op_container_end_page |
34 |
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1766030554091749376 |