Direct Simulation Monte Carlo for astrophysical flows: I. Motivation and
  methodology
  We describe a hybrid Direct Simulation Monte Carlo (DSMC) code for
simultaneously solving the collisional Boltzmann equation for gas and the
collisionless Boltzmann equation for stars and dark matter for problems
important to galaxy evolution. This project is motivated by the need to
understand the controlling dynamics at interfaces between gases of widely
differing densities and temperature, i.e. multiphase media. While more
expensive than hydrodynamics, the kinetic approach does not suffer from
discontinuities and it applies when the continuum limit does not, such as in
the collapse of galaxy clusters and at the interface between coronal halo gas
and a thin neutral gas layer. Finally, the momentum flux is carried,
self-consistently, by particles and this approach explicitly resolves and
thereby captures shocks. The DSMC method splits the solution into two pieces:
1) the evolution of the phase-space flow without collisions; and 2) the
evolution governed the collision term alone without phase-space flow. This
splitting approach makes DSMC an ideal match to existing particle-based n-body
codes. If the mean free path becomes very small compared to any scale of
interest, the method abandons simulated particle collisions and simply adopts
the relaxed solution in each interaction cell consistent with the overall
energy and momentum fluxes. This is functionally equivalent to solving the
Navier-Stokes equations on a mesh. Our implementation is tested using the Sod
shock tube problem and the non-linear development of an Kelvin-Helmholtz
unstable shear layer.
