Ice Sheet Evolution
We will now do some simple ice-sheet evolution experiments using the higher-order model and the 1st-order mass advection scheme we just created. By "simple", I mean coarse resolution, idealized domains with idealized boundary conditions that are actually somewhat non-sensicle. In some sense, we just want to be able to convince ourselves that the combination of a higher-order velocity solution and a mass advection scheme, works.
In the first case, we will allow a parablic-shaped mound of ice to spread out under it's own weight. The non-sensicle part is that we will assume a fixed lateral boundary; the ice sheet margin won't be allowed to move past it's original position. Think of an ice sheet surrounded by a very tall (and very strong) fence. In map view, the ice sheet will eventually take on the shape of a disk of uniform thickness.
In the second case, we will evolve an ice shelf of uniform thickness and temperature, which is confined on three sides and open to the ocean on the fourth side. With no accumulation, which we'll assume, the only thing that can happen is that ice flows out of the shelf front. Eventually, the shelf should thin to zero thickness, but how and when that happens will vary depending on a number of things.