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Modelling and Numerical Simulation of the Dynamics of Glaciers Including 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: guillaume.jouvet@gmail.com
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Abstract

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.

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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References

Barrett, J. W., Liu, W. B.. Quasi-norm error bounds for the finite element approximation of a non-Newtonian flow. Numer. Math. 68 (1994), no. 4, 437–456. CrossRefGoogle Scholar
Benn, D. I., Warren, C. R., Mottram, R. H.. Calving processes and the dynamics of calving glaciers. Earth-Science Reviews, 82 (2007), no. 3-4, 143–179. CrossRefGoogle Scholar
Bonito, A., Picasso, M., Laso, M.. Numerical simulation of 3D viscoelastic flows with free surfaces. J. Comput. Phys., 215 (2006), no. 2, 691–716. CrossRefGoogle Scholar
A. Caboussat, G. Jouvet, M. Picasso, J. Rappaz. Numerical algorithms for free surface flow. Book chapter in CRC volume ’Computational Fluid Dynamics’ (2011).
Caboussat, A., Picasso, M., Rappaz, J.. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J. Comput. Phys., 203 (2005), no. 2, 626–649. CrossRefGoogle Scholar
Farinotti, D., Huss, M., Bauder, A., Funk, M., Truffer, M., A method to estimate ice volume and ice thickness distribution of alpine glaciers. J. Glaciol., 55 (2009), no. 191, 422–430. CrossRefGoogle Scholar
Franca, L. P., Frey, S. L.. Stabilized finite element methods. II. The incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg., 99 (1992), no. 2-3, 209–233. CrossRefGoogle Scholar
The Swiss Glaciers, 1880–2006/07. Tech. Report 1-126, Yearbooks of the Cryospheric Commission of the Swiss Academy of Sciences (SCNAT), 1881–2009, Published since 1964 by Laboratory of Hydraulics, Hydrology and Glaciology (VAW) of ETH Zürich.
Glen, J.W.. The flow law of ice.. IUGG/IAHS Symposium of Chamonix IAHS Publication, 47 (1958), 171183. Google Scholar
R. Greve, H. Blatter. Dynamics of ice sheets and glaciers. Springer Verlag, 2009.
Gudmundsson, G.H.. A three-dimensional numerical model of the confluence area of unteraargletscher, Bernese Alps, Switzerland. J. Glaciol., 45 (1999), no. 150, 219–230. CrossRefGoogle Scholar
M. Huss, A. Bauder, M. Funk, R. Hock. Determination of the seasonal mass balance of four alpine glaciers since 1865. Journal of Geophysical Research, 113 (2008).
K. Hutter. Theoretical glaciology. Reidel, 1983.
G. Jouvet. Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers. Ph.D. thesis, EPF Lausanne, 2010.
Jouvet, G., Huss, M., Blatter, H., Picasso, M., Rappaz, J.. Numerical simulation of rhonegletscher from 1874 to 2100. J. Comp. Phys., 228 (2009), 6426–6439. CrossRefGoogle Scholar
Jouvet, G., Picasso, M., Rappaz, J., Blatter, H.. A new algorithm to simulate the dynamics of a glacier: theory and applications. J. Glaciol., 54 (2008), no. 188, 801–811. CrossRefGoogle Scholar
J. Lemaitre. A course on damage mechanics. Springer, 1992.
Maronnier, V., Picasso, M., Rappaz, J.. Numerical simulation of three-dimensional free surface flows. Internat. J. Numer. Methods Fluids, 42 (2003), no. 7, 697–716. CrossRefGoogle Scholar
A. Pralong. On the instability of hanging glaciers. Ph.D. thesis, ETH Zurich, 2005.
Pralong, A., Funk, M., A level-set method for modeling the evolution of glacier geometry. J. Glaciol., 50 (2004), no. 171, 485–491. CrossRefGoogle Scholar
A. Pralong, M. Funk. Dynamic damage model of crevasse opening and application to glacier calving. J. Geophys. Res., 110 (2005).
Pralong, A., Funk, M., Lüthi, M.. A description of crevasse formation using continuum damage mechanics. Ann. Glaciol., 37 (2003), no. 1, 77–82. CrossRefGoogle Scholar
Scardovelli, R., Zaleski, S.. Direct numerical simulation of free-surface and interfacial flow. Ann. Rev. Fluid Mech., 31 (1999), no. 7, 567–603. CrossRefGoogle Scholar
A. Zryd. Les glaciers en mouvement. Presses polytechniques et universitaires romandes, 2008.