CFL Condition - A snippet of Science

It is been a long time with no post. So I will post an almost meaningless post! I have been working on a poster for AGU, and I am trying to break down a lot of science related content that is prerequisite for the topic of my poster.

So I have posted a figure that I will slap on my poster. The figure to the right shows something called the CFL condition. Courant, Friedrichs and Lewy showed that a spatial grid will not be accurate if the distance something travels is greater than the size of a grid node. So the moving thing is not allowed to move into the next grid cell.

The data I am working with is special because if you have some data that results in traveling too far, like the red and purple arrows, then you need to recompute those regions of the grid using a smaller grid space AND a smaller time step. The traditional model is to recreate the entire grid using a smaller grid and time step. But this approach allows us to focus computation on areas that require more detailed analysis. This changing the grid only where necessary is called Adaptive Mesh Refinement (AMR). Mesh is just a fancier word for grid, for those who haven't heard it before.

I wish I could post about more of the adventures and things I am doing in Korea. But to be fair, I have been spending a lot of time in Korea recently doing all sorts of computer, math, and science related activities. I'm actually looking forward to finishing this poster so I can get back to playing with my little computer programs and playing with scientific results.