A Comparative Study of LBE and DUGKS Methods for Nearly Incompressible Flows (Communications in Computational Physics, 2018)
The lattice Boltzmann equation (LBE) methods (both LBGK and MRT) andthe discrete unified gas-kinetic scheme (DUGKS) are both derived from the Boltzmannequation, but with different consideration in their algorithm construction. With thesame numerical discretization in the particle velocity space, the distinctive modelingof these methods in the update of gas distribution function may introduce differencesin the computational results. In order to quantitatively evaluate the performance ofthese methods in terms of accuracy, stability, and efficiency, in this paper we test LBGK,MRT, and DUGKS in two-dimensional cavity flow and the flow over a square cylinder,respectively. The results for both cases are validated against benchmark solutions.The numerical comparison shows that, with sufficient mesh resolution, the LBE andDUGKS methods yield qualitatively similar results in both test cases. With identicalmesh resolutions in both physical and particle velocity space, the LBE methods aremore efficient than the DUGKS due to the additional particle collision modeling inDUGKS. But the DUGKS is more robust and accurate than the LBE methods in mosttest conditions. Particularly, for the unsteady flow over a square cylinder at Reynoldsnumber 300, with the same mesh resolution it is surprisingly observed that the DUGKScan capture the physical multi-frequency vortex shedding phenomena while the LBGKand MRT fail to get that. Furthermore, the DUGKS is a finite volume method andits computational efficiency can be much improved when a non-uniform mesh in thephysical space is adopted. The comparison in this paper clearly demonstrates the progressiveimprovement of the lattice Boltzmann methods from LBGK, to MRT, up to thecurrent DUGKS, along with the inclusion of more reliable physical process in their algorithmdevelopment. Besides presenting the Navier-Stokes solution, the DUGKS cancapture the rarefied flow phenomena as well with the increasing of Knudsen number.