uu.seUppsala University Publications

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Computational Ice Sheet Dynamics: Error control and efficiencyPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2016 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis, 2016. , p. 46
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1368
##### Keywords [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, id: diva2:919117
##### Public defence

2016-06-03, 2446, Lägerhyddsvägen 2, Uppsala, 10:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Projects

eSSENCEAvailable from: 2016-05-13 Created: 2016-04-13 Last updated: 2016-06-01Bibliographically approved
##### List of papers

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.

1. A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling$(function(){PrimeFaces.cw("OverlayPanel","overlay642574",{id:"formSmash:j_idt570:0:j_idt574",widgetVar:"overlay642574",target:"formSmash:j_idt570:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results$(function(){PrimeFaces.cw("OverlayPanel","overlay682615",{id:"formSmash:j_idt570:1:j_idt574",widgetVar:"overlay682615",target:"formSmash:j_idt570:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method$(function(){PrimeFaces.cw("OverlayPanel","overlay885244",{id:"formSmash:j_idt570:2:j_idt574",widgetVar:"overlay885244",target:"formSmash:j_idt570:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation$(function(){PrimeFaces.cw("OverlayPanel","overlay919090",{id:"formSmash:j_idt570:3:j_idt574",widgetVar:"overlay919090",target:"formSmash:j_idt570:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla$(function(){PrimeFaces.cw("OverlayPanel","overlay919089",{id:"formSmash:j_idt570:4:j_idt574",widgetVar:"overlay919089",target:"formSmash:j_idt570:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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