Comparison of numerical schemes for the solution of the ice-thickness equation in a dynamic/thermodynamic ice-sheet model

  • Authors:

  • Ralf Greve;Reinhard Calov

  • Affiliations:

  • Fachbereich Mechanik, Technische Universität Darmstadt, Hochschulstrasse 1, D-64289 Darmstadt, Germany;Potsdam-Institut für Klimafolgenforschung, Postfach 601203, D-14412 Potsdam, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

A general finite-difference marching scheme for the numerical solution of the ice-thickness equation in ice sheets is considered. From this scheme, a variety of explicit, ADI, implicit and over-implicit methods can be derived. These methods are compared for stability and accuracy within the dynamic/thermodynamic ice-sheet model SICOPOLIS for two different problems: (i) a simple axi-symmetric steady-state ice sheet which rests on a flat bedrock, and (ii) the time-dependent paleoglaciation of the northern hemisphere. As expected, over-implicit methods turn out to be most stable. For the simple problem, all schemes provide a good accuracy, whereas for the northern hemisphere simulations, the accuracy of the over-implicit scheme is not satisfactory, so that the implicit technique without overweighing appears favorable for this application.