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Methods for Simulating Collisionless Matter

© Adam Hughes

Last week, we examined numerical methods for simulating collisional matter. This time around we look at simulation techniques for studying collisionless matter.

The general scheme for the simulation of collisionless matter involves modeling the system with a small number of particles in relation to the total actual number in the overall entity of interest (star, beaker, galaxy). The resulting situation is quite familiar to classical dynamicists: the N-body problem.

So, all of the methods that we've come to know and love during our investigation of molecular dynamics and the planets problems apply here. In particular, the basis for a collisionless simulation is a set of partial differential equations integrated over time by some form of PDE solver. As with most classical simulation, the force calculation is the limiting cost factor, and also the distinguishing characteristic of the simulation types.

While direct calculation of pairwise interaction amongst particles is the most rigorous form of force calculation for a classical simulation, it is also the most expensive. For large astrophysical systems the cost quickly becomes prohibitive, and some sort of further approximation must be made. This usually takes the form of particle-mesh methods, wherein each particle feels forces generated by a grid representation of its neighbors. This greatly reduces cost but can also lead to a loss of detail where the density of particle is highest.

As we've seen before, other combinations can be concocted to attempt to overcome these types of problems. In general, this involves treating part of the system as particles and part as a grid, a scheme which can be fine-tuned for each study. In addition to these techniques, other classical dynamics methods such as long-range force cutoffs are often employed. To learn more about these methods, see the articles in this space dealing with molecular dynamics, or check out

http://flash.uchicago.edu/~ricker/resear...

Having discussed simulation methods to handle both collisional and collisionless matter, it should be stated that both must be addressed to conduct a realistic computer simulation study of a cluster of galaxies. Next week, we'll look at how these types of methods are being combined into one simulation scenario for this purpose.

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