Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T04:02:17.532Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.