Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects

G. Jouvet; M. Picasso; J. Rappaz; M. Huss; M. Funk

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 5, page 263-280
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Jouvet, G., et al. "Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects." Mathematical Modelling of Natural Phenomena 6.5 (2011): 263-280. <http://eudml.org/doc/222209>.

@article{Jouvet2011,
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. },
author = {Jouvet, G., Picasso, M., Rappaz, J., Huss, M., Funk, M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {free surface flows; finite elements; volume of fluid; damage mechanics; glaciers; calving},
language = {eng},
month = {8},
number = {5},
pages = {263-280},
publisher = {EDP Sciences},
title = {Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects},
url = {http://eudml.org/doc/222209},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Jouvet, G.
AU - Picasso, M.
AU - Rappaz, J.
AU - Huss, M.
AU - Funk, M.
TI - Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/8//
PB - EDP Sciences
VL - 6
IS - 5
SP - 263
EP - 280
AB - 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.
LA - eng
KW - free surface flows; finite elements; volume of fluid; damage mechanics; glaciers; calving
UR - http://eudml.org/doc/222209
ER -

References

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