  The general characteristics based off-lattice Boltzmann scheme (BKG) proposed
by Bardow et~al.(2006), and the discrete unified gas kinetic scheme (DUGKS) are
two methods that successfully overcome the time step restriction by the
collision time, which is commonly seen in many other kinetic schemes.
Basically, the BKG scheme is a time splitting scheme, while the DUGKS is an
un-split finite volume scheme. In this work, we first perform a theoretical
analysis of the two schemes in the finite volume framework by comparing their
numerical flux evaluations. It is found that the effects of collision term are
considered in the reconstructions of the cell-interface distribution function
in both schemes, which explains why they can overcome the time step restriction
and can give accurate results even as the time step is much larger than the
collision time. The difference between the two schemes lies in the treatment of
the integral of the collision term, in which the Bardow's scheme uses the
rectangular rule while the DUGKS uses the trapezoidal rule. The performance of
the two schemes, i.e., accuracy, stability, and efficiency are then compared by
simulating several two dimensional flows, including the unsteady Taylor-Green
vortex flow, the steady lid-driven cavity flow, and the laminar boundary layer
problem. It is observed that, the DUGKS can give more accurate results than the
BKG scheme. Furthermore, the numerical stability of the BKG scheme decreases as
the Courant-Friedrichs-Lewy (CFL) number approaches to 1, while the stability
of DUGKS is not affected by the CFL number apparently as long as CFL<1. It is
also observed that the BKG scheme is about one time faster than the DUGKS
scheme with the same computational mesh and time step.
