Monday, July 12, 2010

Collision Dynamics and Granular Flows

So my main field of research is numerical simulations of planetary rings. I keep a page on this work on my main site. Recently I've started working with Josh Colwell at the University of Central Florida on a slightly different project. Josh's project is intended to look at particle collisions to help develop our understanding of accretion in the early stages of planet formation. My role is to do some simulations to compare to the experiments.

Originally I was just going to do simulations of particles orbiting in heliocentric space. Another code was going to be used to do direct comparisons with the simulations. However, this summer I decided I could probably do some of that work with my code. I've been working on that and I have posted a few movies showing this work. This morning though I hit a snag that will take some creative thinking to get around. The problem came when I added a larger impactor body into the simulation to strike the pile of glass spheres that had piled up. Adding this larger impactor caused some problems for the parallel locking mechanism that the code uses. First, the code assumes a fairly 2-D distribution of particles. That's a rather safe assumption for rings. It isn't a very good one for these simulations. It also uses a uniform grid which gets really course when I introduce the large particle.

The code is using a kD-tree to efficiently find collisions. That structure is very dynamic. The nodes have good information on relative velocities and the sizes of particles in them. That makes it very good for non-uniform distributions and also for 3-D simulations. However, the locking mechanism doesn't use the tree. This is because locking needs to be very fast. Grids are O(1) with a small coefficient. Trees are O(log n) with a higher coefficient. We don't want the code that checks if collisions are safe to take more time than the code that actually processes the collisions. So the question is, how can we get around this? That will be my creative thinking exercise for the day.