Computational Ice Sheet Dynamics : Error control and efficiency
Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonia...
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Uppsala universitet, Avdelningen för beräkningsvetenskap
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ftuppsalauniv:oai:DiVA.org:uu-283442 2023-05-15T13:37:43+02:00 Computational Ice Sheet Dynamics : Error control and efficiency Ahlkrona, Josefin 2016 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-283442 eng eng Uppsala universitet, Avdelningen för beräkningsvetenskap Uppsala universitet, Numerisk analys Uppsala Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, 1651-6214 1368 http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-283442 urn:isbn:978-91-554-9562-6 info:eu-repo/semantics/openAccess ice sheet modelling stokes equations shallow ice approximation finite element method perturbation expansions non-newtonian fluids free surface flow Doctoral thesis, comprehensive summary info:eu-repo/semantics/doctoralThesis text 2016 ftuppsalauniv 2023-02-23T21:37:28Z Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated. eSSENCE Doctoral or Postdoctoral Thesis Antarc* Antarctic Greenland Ice Sheet Uppsala University: Publications (DiVA) Antarctic Greenland |
institution |
Open Polar |
collection |
Uppsala University: Publications (DiVA) |
op_collection_id |
ftuppsalauniv |
language |
English |
topic |
ice sheet modelling stokes equations shallow ice approximation finite element method perturbation expansions non-newtonian fluids free surface flow |
spellingShingle |
ice sheet modelling stokes equations shallow ice approximation finite element method perturbation expansions non-newtonian fluids free surface flow Ahlkrona, Josefin Computational Ice Sheet Dynamics : Error control and efficiency |
topic_facet |
ice sheet modelling stokes equations shallow ice approximation finite element method perturbation expansions non-newtonian fluids free surface flow |
description |
Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated. eSSENCE |
format |
Doctoral or Postdoctoral Thesis |
author |
Ahlkrona, Josefin |
author_facet |
Ahlkrona, Josefin |
author_sort |
Ahlkrona, Josefin |
title |
Computational Ice Sheet Dynamics : Error control and efficiency |
title_short |
Computational Ice Sheet Dynamics : Error control and efficiency |
title_full |
Computational Ice Sheet Dynamics : Error control and efficiency |
title_fullStr |
Computational Ice Sheet Dynamics : Error control and efficiency |
title_full_unstemmed |
Computational Ice Sheet Dynamics : Error control and efficiency |
title_sort |
computational ice sheet dynamics : error control and efficiency |
publisher |
Uppsala universitet, Avdelningen för beräkningsvetenskap |
publishDate |
2016 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-283442 |
geographic |
Antarctic Greenland |
geographic_facet |
Antarctic Greenland |
genre |
Antarc* Antarctic Greenland Ice Sheet |
genre_facet |
Antarc* Antarctic Greenland Ice Sheet |
op_relation |
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, 1651-6214 1368 http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-283442 urn:isbn:978-91-554-9562-6 |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1766096925096935424 |