Browsing University of Alaska Fairbanks by Subject "Stokes flow"
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Exact and numerical solutions for stokes flow in glaciersWe begin with an overview of the fluid mechanics governing ice flow. We review a 1985 result due to Balise and Raymond giving exact solutions for a glaciologically-relevant Stokes problem. We extend this result by giving exact formulas for the pressure and for the basal stress. This leads to a theorem giving a necessary condition on the basal velocity of a gravity-induced flow in a rectangular geometry. We describe the finite element method for solving the same problem numerically. We present a concise implementation using FEniCS, a freely-available software package, and discuss the convergence of the numerical method to the exact solution. We describe how to fix an error in a recent published model.