# André Löfgren: Towards a stable ice sheet solver

**Time: **
Wed 2020-02-19 14.00 - 15.00

**Lecturer: **
André Löfgren

**Location: **
Kräftriket, house 5, room 31

### Abstract

The rate at which large scale ice sheets, such as those found on Greenland and Antarctica, lose or gain mass is determined by a balancing between accumulation of ice on the surface and ice flowing into the ocean. When the ice reaches the ocean it begins to melt due to heat exchange with the warmer ocean water. Eventually large chunks of ice in contact with the water breaks free from the rest of the ice sheet in a process known as calving.

In order to understand the rate at which the ice sheet is losing mass one has to consider its dynamics. Ice is as a very slow moving, highly viscous, non-newtonian fluid and as such is most accurately described by the full Stoke’s equation. Time dependence is taken into account by coupling the Stoke’s equation to the so called free surface equation, which describes how the free surface boundary of the ice sheet is advected due to the Stoke’s velocity field.

A problem with this system is that it is numerically quite unstable and has a very strict time step constraint, where very small time steps are needed in order to have a stable solver. This constitutes a severe limitation for making long term predictions as the expensive nonlinear Stoke's equation has to be solved in each time step.

By adding an additional term to the weak form of the Stoke’s equation we achieved stability for time steps 10-20 times larger than without stabilization. This stabilization technique is straightforward to implement into existing code and does not result in significantly larger computation times or memory usage.