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

Performance evaluation of the general characteristics based off-lattice  Boltzmann and DUGKS methods for low speed continuum flows: A comparative  study