  Molecular reflections on usual wall surfaces can be statistically described
by the Maxwell diffuse reflection model, which has been successfully applied in
the DSBGK simulations. We develop the DSBGK algorithm to implement the
Cercignani-Lampis-Lord (CLL) reflection model, which is widely applied to
polished surfaces and used particularly in modeling space shuttles to predict
the heat and force loads exerted by the high-speed flows around the surfaces.
We also extend the DSBGK method to simulate gas mixtures and high contrast of
number densities of different components can be handled at a cost of memory
usage much lower than that needed by the DSMC simulations because the average
numbers of simulated molecules of different components per cell can be equal in
the DSBGK simulations.
