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
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
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