Computational Ice Sheet Dynamics - Error control and efficiency.

Ahlkrona, Josefin (2016) Computational Ice Sheet Dynamics - Error control and efficiency. (PhD/ Doctoral thesis), Uppsala University, Uppsala, Sweden, 46 pp.

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Abstract

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.

Document Type: Thesis (PhD/ Doctoral thesis)
Thesis Advisors: UNSPECIFIED
Keywords: ice sheet modelling, stokes equations, shallow ice approximation, finite element method, perturbation expansions, non-newtonian fluids, free surface flow
Research affiliation: Kiel University
Open Access Journal?: Yes
Date Deposited: 05 Oct 2017 10:15
Last Modified: 01 Feb 2019 15:12
URI: http://oceanrep.geomar.de/id/eprint/39665

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