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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
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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf