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I'm investigating adaptive finite difference techniques applied to computational glaciology. Computional models of the Western Antarctic Ice Sheet face a challenge of length scales: while the ice sheet extends across hundreds of kilometres, its evolution is affected by structures which change over much finer length scales. These are grounding lines, marking the divide bewteen ice seated on rock and ice floating on water, and ice streams, narrow channels of rapidly flowing ice. It would be impractical, or at least inefficient, to treat the whole of the ice sheet on the finest scale, so the idea is to start with a coarse picture, and from there decide which regions must be resolved in more detail, and by how much.
In the figure above, we see a simulated coefficient of drag at the basal of the ice, C, under Pine Island Glacier, a few years into a rapid retreat. Where is it zero (blue) the ice is floating, elsewhere it is in contact with the bedrock. The region around the grounding line is rather finely resolved (the mesh spacing is 250m), elsewhere, the mesh is coarse (with spacing 4km). If the grouding line is treated at a coarse resolution, it does not migrate (or migrates too slowly).
Previously, I was interested in the computational physics of liquid crystals. Perhaps surpisingly, they have something in common with large ice sheets: disparate length scales. My most recent work was on adaptive finite element techiques, using them to resolve the motion of tiny (10 nm) topological defects at the same time as elastic deformations over a relatively large scale (1000nm) .
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