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Effects of numerical implementations of the impenetrability condition on non-linear Stokes flow: applications to ice dynamics
Stockholm University, Faculty of Science, Department of Physical Geography.ORCID iD: 0000-0003-4310-4873
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The basal sliding of glaciers and ice sheets can constitute a large part of the total observed ice velocity, in particular in dynamically active areas. It is therefore important to accurately represent this process in numerical models. The condition that the sliding velocity should be tangential to the bed is realized by imposing an impenetrability condition at the base. We study the, in glaciological literature used, numerical implementations of the impenetrability condition for non-linear Stokes flow with Navier's slip on the boundary. Using the finite element method, we enforce impenetrability by: a local rotation of the coordinate system (strong method), a Lagrange multiplier method enforcing zero average flow across each facet (weak method) and an approximative method that uses the pressure variable as a Lagrange multiplier for both incompressibility and impenetrability. An analysis of the latter shows that it relaxes the incompressibility constraint, but enforces impenetrability approximately if the pressure is close to the normal component of the stress at the bed. Comparing the methods numerically using a method of manufactured solutions unexpectedly leads to similar convergence results. However, we find that, for more realistic cases, in areas of high sliding or varying topography the velocity field simulated by the approximative method differs from that of the other methods by approx. 1% (two dimensional flow) and  > 5% when compared to the strong method (three-dimensional flow). In this study the strong method, which is the most commonly used in numerical ice sheet models, emerges as the preferred method due to its stable properties (compared to the weak method in three dimensions) and ability to well enforce the impenetrability condition.

Keyword [en]
Non-linear Stokes, slip boundary conditions, finite element method, Lagrange multiplier method
National Category
Geosciences, Multidisciplinary
Research subject
Physical Geography
Identifiers
URN: urn:nbn:se:su:diva-141640OAI: oai:DiVA.org:su-141640DiVA: diva2:1087902
Available from: 2017-04-10 Created: 2017-04-10 Last updated: 2017-04-27Bibliographically approved
In thesis
1. Basal boundary conditions, stability and verification in glaciological numerical models
Open this publication in new window or tab >>Basal boundary conditions, stability and verification in glaciological numerical models
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

To increase our understanding of how ice sheets and glaciers interact with the climate system, numerical models have become an indispensable tool. However, the complexity of these systems and the natural limitation in computational power is reflected in the simplifications of the represented processes and the spatial and temporal resolution of the models. Whether the effect of these limitations is acceptable or not, can be assessed by theoretical considerations and by validating the output of the models against real world data. Equally important is to verify if the numerical implementation and computational method accurately represent the mathematical description of the processes intended to be simulated. This thesis concerns a set of numerical models used in the field of glaciology, how these are applied and how they relate to other study areas in the same field.

The dynamical flow of glaciers, which can be described by a set of non-linear partial differential equations called the Full Stokes equations, is simulated using the finite element method. To reduce the computational cost of the method significantly, it is common to lower the order of the used elements. This results in a loss of stability of the method, but can be remedied by the use of stabilization methods. By numerically studying different stabilization methods and evaluating their suitability, this work contributes to constraining the values of stabilization parameters to be used in ice sheet simulations. Erroneous choices of parameters can lead to oscillations of surface velocities, which affects the long term behavior of the free-surface ice and as a result can have a negative impact on the accuracy of the simulated mass balance of ice sheets.

The amount of basal sliding is an important component that affects the overall dynamics of the ice. A part of this thesis considers different implementations of the basal impenetrability condition that accompanies basal sliding, and shows that methods used in literature can lead to a difference in velocity of 1% to 5% between the considered methods.

The subglacial hydrological system directly influences the glacier's ability to slide and therefore affects the velocity distribution of the ice. The topology and dominant mode of the hydrological system on the ice sheet scale is, however, ill constrained. A third contribution of this thesis is, using the theory of R-channels to implement a simple numerical model of subglacial water flow, to show the sensitivity of subglacial channels to transient processes and that this limits their possible extent. This insight adds to a cross-disciplinary discussion between the different sub-fields of theoretical, field and paleo-glaciology regarding the characteristics of ice sheet subglacial hydrological systems. In the study, we conclude by emphasizing areas of importance where the sub-fields have yet to unify: the spatial extent of channelized subglacial drainage, to what degree specific processes are connected to geomorphic activity and the differences in spatial and temporal scales.

As a whole, the thesis emphasizes the importance of verification of numerical models but also acknowledges the natural limitations of these to represent complex systems. Focusing on keeping numerical ice sheet and glacier models as transparent as possible will benefit end users and facilitate accurate interpretations of the numerical output so it confidently can be used for scientific purposes.

Place, publisher, year, edition, pages
Stockholm: Department of Physical Geography, Stockholm University, 2017. 79 p.
Series
Dissertations from the Department of Physical Geography, ISSN 1653-7211 ; 62
Keyword
Glaciology, subglacial hydrology, ice sheet modeling, basal boundary conditions, non-linear Stokes flow
National Category
Physical Geography
Research subject
Physical Geography
Identifiers
urn:nbn:se:su:diva-141641 (URN)978-91-7649-778-4 (ISBN)978-91-7649-779-1 (ISBN)
Public defence
2017-05-31, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 13:00 (English)
Opponent
Supervisors
Projects
Greenland Analogue Project
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.

Available from: 2017-05-08 Created: 2017-04-11 Last updated: 2017-05-03Bibliographically approved

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