Geodesic
Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects
G. Jouvet1 ; M. Picasso1 ; J. Rappaz1 ; M. Huss2 ; M. Funk3
1 Mathematics Institute of Computational Science and Engineering, EPFL, 1015 Lausanne, Switzerland
2 Department of Geosciences, University of Fribourg, 1700 Fribourg, Switzerland
3 Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETHZ, 8092 Zurich, Switzerland
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 5, pp. 263-280

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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.
DOI : 10.1051/mmnp/20116510

G. Jouvet 1 ; M. Picasso 1 ; J. Rappaz 1 ; M. Huss 2 ; M. Funk 3

1 Mathematics Institute of Computational Science and Engineering, EPFL, 1015 Lausanne, Switzerland
2 Department of Geosciences, University of Fribourg, 1700 Fribourg, Switzerland
3 Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETHZ, 8092 Zurich, Switzerland 
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G. Jouvet; M. Picasso; J. Rappaz; M. Huss; M. Funk. Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 5, pp. 263-280. doi: 10.1051/mmnp/20116510

[1] J. W. Barrett, W. B. Liu Numer. Math. 1994 437 456

[2] D. I. Benn, C. R. Warren, R. H. Mottram Earth-Science Reviews 2007 143 179

[3] A. Bonito, M. Picasso, M. Laso J. Comput. Phys. 2006 691 716

[4] A. Caboussat, G. Jouvet, M. Picasso, J. Rappaz. Numerical algorithms for free surface flow. Book chapter in CRC volume ’Computational Fluid Dynamics’ (2011).

[5] A. Caboussat, M. Picasso, J. Rappaz J. Comput. Phys. 2005 626 649

[6] D. Farinotti, M. Huss, A. Bauder, M. Funk, M. Truffer J. Glaciol. 2009 422 430

[7] L. P. Franca, S. L. Frey Comput. Methods Appl. Mech. Engrg. 1992 209 233

[8] 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.

[9] J.W. Glen IUGG/IAHS Symposium of Chamonix IAHS Publication 1958

[10] R. Greve, H. Blatter. Dynamics of ice sheets and glaciers. Springer Verlag, 2009.

[11] G.H. Gudmundsson J. Glaciol. 1999 219 230

[12] 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).

[13] K. Hutter. Theoretical glaciology. Reidel, 1983.

[14] G. Jouvet. Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers. Ph.D. thesis, EPF Lausanne, 2010.

[15] G. Jouvet, M. Huss, H. Blatter, M. Picasso, J. Rappaz J. Comp. Phys. 2009 6426 6439

[16] G. Jouvet, M. Picasso, J. Rappaz, H. Blatter J. Glaciol. 2008 801 811

[17] J. Lemaitre. A course on damage mechanics. Springer, 1992.

[18] V. Maronnier, M. Picasso, J. Rappaz Internat. J. Numer. Methods Fluids 2003 697 716

[19] A. Pralong. On the instability of hanging glaciers. Ph.D. thesis, ETH Zurich, 2005.

[20] A. Pralong, M. Funk J. Glaciol. 2004 485 491

[21] A. Pralong, M. Funk. Dynamic damage model of crevasse opening and application to glacier calving. J. Geophys. Res., 110 (2005).

[22] A. Pralong, M. Funk, M. Lüthi Ann. Glaciol. 2003 77 82

[23] R. Scardovelli, S. Zaleski Ann. Rev. Fluid Mech. 1999 567 603

[24] A. Zryd. Les glaciers en mouvement. Presses polytechniques et universitaires romandes, 2008.

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