Published: Nov. 10, 2015

Fluidity based FOSLS Formulation of Nonlinear Stokes Flow for Glaciers

Jeffrey Allen

Applied MathematicsUniversity of Colorado Boulder

Date and time: 

Tuesday, November 10, 2015 - 11:00am

Location: 

GRVW 105

Abstract: 

This talk is about modeling glaciers and ice sheets using a full nonlinear Stokes method. The first part will be a quick discussion about determine the basal topography of the Kennicott glacier using high resolution satellite imagery. The second part describes a First-order System Least Squares (FOSLS) formulation of a nonlinear Stokes flow model.

In Glen's law, the most commonly used constitutive equation for ice rheology, the ice viscosity becomes infinite as the velocity gradients (strain rates) approach zero, which typically occurs near the ice surface where deformation rates are low, or when the basal slip velocities are high.  The computational difficulties associated with the infinite viscosity are often overcome by an arbitrary modification of Glen's law that bounds the maximum viscosity.  The Stress-Vorticity-Fluidity formulation exploits the fact that only the product of the viscosity and strain rate appears in the nonlinear Stokes problem, a quantity that in fact approaches zero as the strain rate goes to zero.  This formulation is expressed in terms of a new set of variables and overcomes the problem of infinite viscosity.  The new formulation is well posed and $H^1$ elliptic away from spatial locations where the velocity gradients are zero.  A Nested Iteration (NI) Newton-FOSLS approach is used to solve the nonlinear Stokes problems, in which most of the iterations are performed on the coarsest grid. This fluidity based formulation demonstrate optimal finite element convergence and involves linear systems that are more amenable to solution by AMG.