Summer is over and I would like to report on a student’s research project that I especially liked. The full title is of the project was

Modeling Heat Transfer on Various Grids with Discrete Exterior Calculus by Julie Lang.

The main issue we ended up studying was isotropy as heat is supposed to transfer equally in all directions. Since no grid is isotropic, this is a big issue. Every time, we would start with all the initial heat concentrated in a single cell and then saw if, after many iterations, the shape of the heat function is circular. If it wasn’t, the model was simply wrong! Every time we had to come up with a modification and then continue with trial and error. Not very rigorous but fascinating scientifically. The last grid was rhomboidal and we were left with an oval, unfortunately…

It’s a good story and an interesting read. This is the link to the project page.