An adaptive finite volume solver for ice sheets and glaciers

Abstract

We have developed a new adaptive finite volume scheme for numerical simulations of ice sheets and glaciers. The mathematical basis of the adaptive solver is represented by the finite volume method and irregular Voronoi cell grids. Evaluation of spatial derivatives are obtained at cell edges from approximating the ice surface elevation locally by secondorder polynomials following a least squares approach. The proposed scheme includes a simple and accurate method for handling discontinuities in ice thickness gradients along ice margins. The flexibility of the Voronoi cell structure allows for local mesh refinement in selected areas. We show how increased mesh density along a steep ice margin may considerably increase overall numerical accuracy of an ice sheet simulation. Although the numerical scheme is not restricted to ice sheet representations using the shallow ice approximation (SIA), we here use analytical SIA solutions to test the accuracy of the method. Copyright 2010 by the American Geophysical Union.