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Methods for Simulating Collisional Matter

© Adam Hughes

Last week we discussed collisional and noncollisional matter, such as may be found in galaxy clusters, and the basic principles for studying these entities numerically. This week, we take a more in-depth look at specific computational methods for examining collisional matter.

Although collisional matter, such as astrophysical gas, is much more tightly packed than noncollisional matter, there often is still a lot of space between particles. Because of this, the gas is said to be highly compressible, and collisions happen at very high speeds. Under these conditions shock waves can form. Shock waves are regions in space where the density, pressure and kinetic energy of matter change extremely quickly. Material flows into a shock-wave region at supersonic speeds and away from the region at subsonic speeds. This rapid deceleration means that a great deal of matter is compressed into the region at the front of the wave. To model this situation, high-resolution numerical methods are needed to retain the resulting fine-structure. The two techniques generally used to study this phenomenon in astrophysical hydrodynamics are the Piecewise-Parabolic Method (PPM) and Smoothed Particle Hydrodynamics.

The PPM is a finite-volume technique which allows for fine-structure simulation via the use of a grid. The variables associated with each grid point are updated using the four nearest grid points in each spatial direction. This method has been successfully parallelized, with good speedup achieved. A drawback, however, is that adaptive gridding must be used if PPM is to be employed across length scales (near the shock front and removed from it). For more discussion on PPM, check out any of these web sites:

http://flash.uchicago.edu/~ricker/resear...
http://webserv.gsfc.nasa.gov/neumann/ppm...
http://www.cineca.it/editions/ssc97/html...

Smoothed Particle Hydrodynamics (SPH), on the other hand, is capable of accommodating a wide range of length scales. Particles vary in size and pressure depending on the localized density of the system, automatically allowing different concentrations of matter to exist simultaneously in the same system. On the downside, SPH cannot handle shock waves very well because the particle mass is limited in this scheme. To read more about this method, see

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

Next week, we'll investigate methods for simulating systems of collisionless matter.

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