Numerical simulation of the motion of a three-dimensional glacier
Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 1-28.

The motion of a three-dimensional glacier is considered. Ice is modeled as an incompressible non-Newtonian fluid. At each time step, given the shape of the glacier, a nonlinear elliptic system has to be solved in order to obtain the two components of the horizontal velocity field. Then, the shape of the glacier is updated by solving a transport equation. Finite element techniques are used to compute the velocity field and to solve the transport equation. Numerical results are compared to experiments on Storglaciaren (Sweden) between 1959 and 1990.

DOI: 10.5802/ambp.236
Classification: 65N30, 76M10
Keywords: glacier, ice, non-Newtonian fluid, finite elements
Marco Picasso 1; Jacques Rappaz 1; Adrian Reist 1

1 Institut d’analyse et calcul scientifique, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
     author = {Marco Picasso and Jacques Rappaz and Adrian Reist},
     title = {Numerical simulation of the motion of a three-dimensional glacier},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {1--28},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     number = {1},
     year = {2008},
     doi = {10.5802/ambp.236},
     mrnumber = {2418010},
     zbl = {1141.76038},
     language = {en},
     url = {}
AU  - Marco Picasso
AU  - Jacques Rappaz
AU  - Adrian Reist
TI  - Numerical simulation of the motion of a three-dimensional glacier
JO  - Annales mathématiques Blaise Pascal
PY  - 2008
SP  - 1
EP  - 28
VL  - 15
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  -
DO  - 10.5802/ambp.236
LA  - en
ID  - AMBP_2008__15_1_1_0
ER  - 
%0 Journal Article
%A Marco Picasso
%A Jacques Rappaz
%A Adrian Reist
%T Numerical simulation of the motion of a three-dimensional glacier
%J Annales mathématiques Blaise Pascal
%D 2008
%P 1-28
%V 15
%N 1
%I Annales mathématiques Blaise Pascal
%R 10.5802/ambp.236
%G en
%F AMBP_2008__15_1_1_0
Marco Picasso; Jacques Rappaz; Adrian Reist. Numerical simulation of the motion of a three-dimensional glacier. Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 1-28. doi : 10.5802/ambp.236.

[1] Olaf Albrecht; Peter Jansson; Heinz Blatter Modelling Glacier Response to Measured Mass-Balance Forcing, Annals of Glaciology, Volume 31 (2000), pp. 91-96 | DOI

[2] R. Alley; P.U. Clark; P. Huybrechts; I. Joughin Ice sheets and sea-level change, Science, Volume 310 (2005), pp. 456-460 | DOI

[3] Heinz Blatter Velocity and Stress Fields in Grounded Glaciers: A Simple Algorithm for Including Deviatoric Stress Gradients, Journal of Glaciology, Volume 41 (1995) no. 138, pp. 333-344

[4] D. Boffi; L. Gastaldi Stability and geometric conservation laws for ALE formulations, Comput. Methods Appl. Mech. Engrg., Volume 193 (2004) no. 42-44, pp. 4717-4739 | DOI | MR | Zbl

[5] Alexander N. Brooks; Thomas J. R. Hughes Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., Volume 32 (1982) no. 1-3, pp. 199-259 FENOMECH ’81, Part I (Stuttgart, 1981) | DOI | MR | Zbl

[6] G.F. Carey; W. Barth; J.A. Woods; B.S. Kirk; M.L. Anderson; S. Chow; W. Bangerth Modelling error and constitutive relations in simulation of flow and transport, Int. J. Numer. Meth. Fluids, Volume 46 (2004), pp. 1211-1236 | DOI | MR | Zbl

[7] Graham F. Carey Computational grids, Series in Computational and Physical Processes in Mechanics and Thermal Sciences, Taylor & Francis, Washington, DC, 1997 (Generation, adaptation, and solution strategies) | MR | Zbl

[8] S. Chow; G.F. Carey; M.L. Anderson Finite element approximations of a glaciology problem, Math. Model. Numer. Anal., Volume 38 (741–756) no. 5, pp. 2004 | Numdam | MR | Zbl

[9] J. Colinge; H. Blatter Stress and velocity fields in glaciers: Part I. Finite difference schemes for higher-order glacier models, Journal of Glaciology, Volume 44 (1998) no. 149, pp. 457-466

[10] J. Colinge; J. Rappaz A strongly nonlinear problem arising in glaciology, Math. Model. Numer. Anal., Volume 33 (1999) no. 2, pp. 395-406 | DOI | Numdam | MR | Zbl

[11] K. Erikson; D. Estep; P. Hansbo; C. Johnson Computational Differential Equations, Cambridge University Press, 1996 | Zbl

[12] A. C. Fowler A mathematical analysis of glacier surges, SIAM J. Appl. Math., Volume 49 (1989) no. 1, pp. 246-263 | DOI | MR | Zbl

[13] A. C. Fowler Glaciers and ice sheets, The mathematics of models for climatology and environment (Puerto de la Cruz, 1995) (NATO ASI Ser. Ser. I Glob. Environ. Change), Volume 48, Springer, Berlin, 1997, pp. 301-336 | MR | Zbl

[14] R. Glowinski; J. Rappaz Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology, Math. Model. Numer. Anal., Volume 37 (175–186) no. 1, pp. 2003 | Numdam | MR | Zbl

[15] G.H. Gudmundsson A three-dimensional numerical model of the confluence area of unteraargletscher, bernese alps, Switzerland, J. Glaciol, Volume 45 (1999) no. 150, pp. 219-230 | DOI

[16] U. C. Herzfeld; M. G. Eriksson; P. Holmlund On the Influence of Kriging Parameters on the Cartographic Output - A study in Mapping Subglacial Topography, Mathematical Geol., Volume 27 (1993) no. 7, pp. 881-900 | DOI

[17] P. Holmlund Maps of Storglaciären and their use in glacier monitoring studies. (incl. 2 maps of the glaciers in the Tarfala valley in the scale 1:10 000), Geogr. Ann., Volume 78 A (1996) no. 2–3, pp. 193-196 | DOI

[18] P. Huybrechts; T. Payne; the EISMINT intercomparison group The EISMINT benchmark for testing ice-sheet models, Annals of Glaciology, Volume 23 (1996)

[19] R. Löner; C. Yang Improved ALE mesh velocities for moving boundaries, Comm. Num. Meth. Eng., Volume 12 (1996), pp. 599-608 | DOI | Zbl

[20] C. Martin; F. Navarro; J. Otero; M.L. Cuadrado; M.L. Corcuera Three-dimensional modelling of the dynamics of Johnsons Glacier, Livingston Island, Antarctica, Annals of Glaciology, Volume 39 (2004), pp. 1-8 | DOI

[21] Marco Picasso; Jacques Rappaz; Adrian Reist; Heinz Blatter; Martin Funk Numerical simulation of the motion of a two-dimensional glacier, Int. J. Numer. Meth. Eng., Volume 60 (2004), pp. 995-1009 | DOI | MR | Zbl

[22] J. Rappaz; A. Reist Mathematical and Numerical Analysis of a Three Dimensional Fluid Flow Model in Glaciology, M3AS, Volume 15 (2005) no. 1, pp. 37-52 | MR

[23] A. Reist Mathematical analysis and numerical simulation of the motion of a glacier, Ecole Polytechnique Fédérale de Lausanne (2005) (Ph. D. Thesis)

[24] I. Robertson; S. Sherwin Free-surface flow simulation using hp/spectral elements, J. Comp. Phys., Volume 155 (1999), pp. 26-53 | DOI | MR | Zbl

Cited by Sources: