Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique

Abstract

ABSTRACT. The two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions , however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6-7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply. REsuME. Modelisation il deux dimensions en fonction du temps d'une masse de glace de forme quelconque par la technique des elements finis . L'ecoulement bidimensionnel fonction du temps d'une masse de glace de forme quelconque peut-etre modelise avec succes par la technique des elements finis it l'aide d'un petit calculateur. Une generation automatique du maillage simplifie grandement la preparation des donnees et optimise les simulations numeriques.

Plane ice-sheet flow with evolving orthotopic fabric

“…The most common simplifications are: (1) the reduction of geometrical dimensionality by taking advantage of symmetries in a flow field and solving either a plane or an axi-symmetric problem, and (2) the assumption of isotropic behaviour for the ice. Such an approach, in which Stokes’equations for an incompressible viscous fluid are solved with the constitutive relation in the form of Glen’s flow law, was employed, for instance, by Hooke and others (1979), Raymond (1983), Hodge (1985), Hanson (1995) and Hvidberg (1996).…”

A One-Dimensional Finite-Element Model for Two-Dimensional Glacier Flow

“…As indicated previously, during the past several years there has been a move in glaciology toward two-dimensional finite-element modelling of large ice-mass dynamic phenomena, including: creep analysis due to gravity loading (Emery, 1978; Hooke and others, 1979; Hodge, 1985; Nguyen, unpublished); thermal analysis (Hooke and others, 1979); creep and fracture simulation (Chan, unpublished); particle-path determination (Stolle and Killeavy, 1986); and large ice-mass instability (Stolle and Mirza, 1986). By no means does this list exhaust all finite-element literature in glaciology.…”

Thermal Response of a Small Ice Cap to Climatic Forcing

“…The shape functions and integration method used in that temperature model have been adapted to the entire calculation here. A much different approach to the velocity calculations has been described by Hodge (1985). Hodge used quadratic shape functions on elements defined by nine nodes in a three-by-three array.…”