Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011Complex Fluids
|Page(s)||263 - 280|
|Published online||10 August 2011|
Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects
Mathematics Institute of Computational Science and Engineering,
2 Department of Geosciences, University of Fribourg, 1700 Fribourg, Switzerland
3 Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETHZ, 8092 Zurich, Switzerland
⋆ Corresponding author. E-mail: firstname.lastname@example.org
A numerical model to compute the dynamics of glaciers is presented. Ice damage due to cracks or crevasses can be taken into account whenever needed. This model allows simulations of the past and future retreat of glaciers, the calving process or the break-off of hanging glaciers. All these phenomena are strongly affected by climate change.
Ice is assumed to behave as an incompressible fluid with nonlinear viscosity, so that the velocity and pressure in the ice domain satisfy a nonlinear Stokes problem. The shape of the ice domain is defined using the volume fraction of ice, that is one in the ice region and zero elsewhere. The volume fraction of ice satisfies a transport equation with a source 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 function D 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 D satisfies a transport equation with nonlinear source terms to model cracks formation or healing.
A splitting scheme allows transport and diffusion phenomena to be decoupled. Two fixed grids are used. The transport equations are solved on an unstructured grid of small cubic cells, thus allowing numerical diffusion of the volume fraction of ice to be reduced as much as possible. The nonlinear Stokes problem is solved on an unstructured mesh of tetrahedrons, larger than the cells, using stabilized finite elements.
Two computations are presented at different time scales. First, the dynamics of Rhonegletscher, Swiss Alps, are investigated in 3D from 2007 to 2100 using several climatic scenarios and without considering ice damage. Second, ice damage is taken into account in order to reproduce the calving process of a 2D glacier tongue submerged by water.
Mathematics Subject Classification: 76A05 / 76D27
Key words: free surface flows / finite elements / volume of fluid / damage mechanics / glaciers / calving
© EDP Sciences, 2011
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