  In this paper we develop a direct simulation Monte Carlo (DSMC) method for
simulating highly nonequilibrium dynamics of nearly degenerate ultra-cold
gases. We show that our method can simulate the high-energy collision of two
thermal clouds in the regime observed in experiments [Thomas, et al. Phys. Rev.
Lett. \textbf{93}, 173201 (2004)], which requires the inclusion of beyond
s-wave scattering. We also consider the long-time dynamics of this system,
demonstrating that this would be a practical experimental scenario for testing
the Boltzmann equation and studying rethermalization.
