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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Volume 4, issue 4
Geosci. Model Dev., 4, 1133–1149, 2011
https://doi.org/10.5194/gmd-4-1133-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
Geosci. Model Dev., 4, 1133–1149, 2011
https://doi.org/10.5194/gmd-4-1133-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.

Development and technical paper 19 Dec 2011

Development and technical paper | 19 Dec 2011

Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

J. J. Fürst1, O. Rybak1, H. Goelzer1, B. De Smedt1, P. de Groen2, and P. Huybrechts1 J. J. Fürst et al.
  • 1Earth System Sciences & Department of Geography, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, Belgium
  • 2Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, Belgium

Abstract. We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation.

The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented.

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