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Modelling and Numerical Simulation of the Dynamics of GlaciersIncluding Local Damage Effects

Published online by Cambridge University Press:  10 August 2011

G. Jouvet ,
M. Picasso ,
J. Rappaz ,
M. Huss  and
M. Funk
G. Jouvet*
Affiliation:
Mathematics Institute of Computational Science and Engineering, EPFL, 1015 Lausanne, Switzerland
M. Picasso
Affiliation:
Mathematics Institute of Computational Science and Engineering, EPFL, 1015 Lausanne, Switzerland
J. Rappaz
Affiliation:
Mathematics Institute of Computational Science and Engineering, EPFL, 1015 Lausanne, Switzerland
M. Huss
Affiliation:
Department of Geosciences, University of Fribourg, 1700 Fribourg, Switzerland
M. Funk
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETHZ, 8092 Zurich, Switzerland
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

A numerical model to compute the dynamics of glaciers is presented. Ice damage due tocracks or crevasses can be taken into account whenever needed. This model allowssimulations of the past and future retreat of glaciers, the calving process or thebreak-off of hanging glaciers. All these phenomena are strongly affected by climatechange.

Ice is assumed to behave as an incompressible fluid with nonlinear viscosity, so that thevelocity and pressure in the ice domain satisfy a nonlinear Stokes problem. The shape ofthe ice domain is defined using the volume fraction of ice, that is one in the ice regionand zero elsewhere. The volume fraction of ice satisfies a transport equation with asource term on the upper ice-air free surface accounting for ice accumulation or melting.If local effects due to ice damage must be taken into account, the damage functionD is introduced, ranging between zero if no damage occurs and one.Then, the ice viscosity μ in the momentum equation must be replaced by(1 − D)μ. The damage function Dsatisfies a transport equation with nonlinear source terms to model cracks formation orhealing.

A splitting scheme allows transport and diffusion phenomena to be decoupled. Two fixedgrids are used. The transport equations are solved on an unstructured grid of small cubiccells, thus allowing numerical diffusion of the volume fraction of ice to be reduced asmuch as possible. The nonlinear Stokes problem is solved on an unstructured mesh oftetrahedrons, larger than the cells, using stabilized finite elements.

Two computations are presented at different time scales. First, the dynamics ofRhonegletscher, Swiss Alps, are investigated in 3D from 2007 to 2100 using severalclimatic scenarios and without considering ice damage. Second, ice damage is taken intoaccount in order to reproduce the calving process of a 2D glacier tongue submerged bywater.

Keywords

free surface flowsfinite elementsvolume of fluiddamage mechanicsglacierscalving
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 263 - 280
Copyright
© EDP Sciences, 2011

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