A new fully three-dimensional numerical model for ice dynamics

Abstract

The problem of describing ice dynamics has been faced by many researchers; in this paper a fully three-dimensional model for ice dynamics is presented and tested. Using an approach followed by other researchers, ice is considered a non-linear incompressible viscous fluid so that a fluid-dynamic approach can be used. The model is based on the full three-dimensional Stokes equations for the description of pressure and velocity fields, on the Saint-Venant equation for the description of the freesurface time evolution and on a constitutive law derived from Glen's law for the description of ice viscosity. The model computes the complete pressure field by considering both the hydrostatic and hydrodynamic pressure components; it is time-evolutive and uses high-order numerical approximation for equations and boundary conditions. Moreover it can deal with both constant and variable viscosity. Three theoretical tests and two applications to Priestley Glacier, Antarctica, are presented in order to evaluate the performance of the model and to investigate important phenomena of ice dynamics such as the influence of viscosity on pressure and velocity fields, basal sliding and flow over perturbed bedrocks. All these applications demonstrate the importance of treating the complete pressure and stress fields.

Numerical simulation of Rhonegletscher from 1874 to 2100

“…A tetrahedron is said to be iced if at least one of its four vertices has a volume fraction of ice greater than 0. 5 . Also l nÀ1 (respectively a nÀ1 ) is defined by (3), (respectively (8) (17) is sought in the space of continuous functions, piecewise linear on the tetrahedrons of the finite element mesh.…”

A fully 3D finite volume method for incompressible Navier–Stokes equations

“…In all the applications presented here Newtonian uids have been considered; nevertheless the use of particular constitutive laws, e.g. Glen's law for ice, allows the description of the dynamics of non-Newtonian uids [33]. The use of control volumes with inclined faces is also under study and its implementation should lead to an improved description of the free surface evolution and a better approximation of boundary conditions.…”

“…In Figure 3(a) the time history of the ' 2 di erence norm for velocity u and pressure p are presented. The discrete ' 2 norm for velocity is computed by (33) where the outer sum is extended to all control volumes, x, y, z are the dimensions of the control volume, u i andû i are the three components of the numerically computed velocity and of the exact velocity, respectively. The discrete ' 2 norm of the pressure is computed by It can be seen that the di erence norm is always very small and rapidly decreases for increasing time; moreover, no numerical instability or computational error dispersion can be noticed.…”

Derivation of a numerical solution of the 3D coupled velocity field for an ice sheet – ice shelf system, incorporating both full and approximate stress solutions

“…This is a slightly easier approach than applying a stress free condition, as e.g. derived by Deponti et al (2006), but without a significant difference. The atmosphere-ice interface and the ice-water interface at the bottom of the shelf are both taken as free surfaces by imposing:…”