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Computational Ice Sheet Dynamics: Error control and efficiency
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2016. , 46 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1368
Keyword [en]
ice sheet modelling, stokes equations, shallow ice approximation, finite element method, perturbation expansions, non-newtonian fluids, free surface flow
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:uu:diva-283442ISBN: 978-91-554-9562-6 (print)OAI: oai:DiVA.org:uu-283442DiVA: diva2:919117
Public defence
2016-06-03, 2446, Lägerhyddsvägen 2, Uppsala, 10:00 (English)
Opponent
Supervisors
Projects
eSSENCE
Available from: 2016-05-13 Created: 2016-04-13 Last updated: 2016-06-01Bibliographically approved
List of papers
1. A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
Open this publication in new window or tab >>A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
2013 (English)In: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, 417-435 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-205727 (URN)10.1093/qjmam/hbt009 (DOI)000327457200001 ()
Projects
eSSENCE
Available from: 2013-08-09 Created: 2013-08-22 Last updated: 2017-12-06Bibliographically approved
2. Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
Open this publication in new window or tab >>Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
2013 (English)In: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, 2135-2152 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-213571 (URN)10.5194/gmd-6-2135-2013 (DOI)000329050500017 ()
Projects
eSSENCE
Available from: 2013-12-19 Created: 2013-12-28 Last updated: 2017-12-06Bibliographically approved
3. Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
Open this publication in new window or tab >>Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, 1-19 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-269822 (URN)10.1016/j.jcp.2015.12.025 (DOI)000369086700001 ()
Projects
eSSENCE
Available from: 2015-12-17 Created: 2015-12-18 Last updated: 2017-12-01Bibliographically approved
4. The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
Open this publication in new window or tab >>The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
2016 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-006
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-283438 (URN)
Projects
eSSENCE
Available from: 2016-04-19 Created: 2016-04-13 Last updated: 2016-05-16Bibliographically approved
5. A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
Open this publication in new window or tab >>A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
2016 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-005
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-283437 (URN)
Projects
eSSENCE
Available from: 2016-04-19 Created: 2016-04-13 Last updated: 2016-05-16Bibliographically approved

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Ahlkrona, Josefin

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