  The Bhatnagar-Gross-Krook (BGK) model as well as its extensions (ellipsoidal
statistical BGK, Shakhov BGK, unified BGK) are used in particle-based fluid
dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To
this end, different methods are investigated that allow efficient sampling of
the Shakhov and the unified target distribution functions. As a consequence,
particle simulations based on the Shakhov BGK and the unified BGK model are
possible in an efficient way. Furthermore, different energy conservation
schemes are tested for the BGK models. It is shown that the choice of the
energy conservation scheme has a major impact on the quality of the results for
each model. The models are verified with a Couette flow problem at different
Knudsen numbers and wall velocities. Furthermore, the models are compared with
DSMC results of a hypersonic flow around a 70$^\circ$ blunted cone. It is shown
that the unified BGK model is able to reproduce rarefied gas phenomena.
Furthermore, it is shown that the difference in the reproduction of shock
structure is not significant between the ellipsoidal statistical BGK and
Shakhov BGK model for the flow around a 70$^\circ$ blunted cone and
significantly depends on the energy conservation method. The choice of the
energy conservation method is especially crucial for the Shakhov model whereas
the ellipsoidal statistical BGK model is much more robust concerning the energy
conservation scheme. Additionally, a computational time study is done to show
the efficiency of BGK-based simulations for low Knudsen number flows compared
with DSMC.
