Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 333, Issue -, Pages 227-246Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.11.051
Keywords
Off-lattice Boltzmann method; Finite volume method; Discrete Boltzmann equation; Kinetic scheme
Funding
- National Science Foundation of China [51125024, 11602091]
- Fundamental Research Funds for the Central Universities [2014TS119]
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The general characteristics based off-lattice Boltzmann scheme proposed by Bardow et al. [1] (hereafter Bardow's scheme) and the discrete unified gas kinetic scheme (DUGKS) [2] are two methods that successfully overcome the time step restriction by the collision time, which is commonly seen in many other kinetic schemes. 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 effect of collision term is considered in the evaluation 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 when evaluating the cell interface distribution function, in which Bardow's scheme uses the rectangular rule while 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, DUGKS can give more accurate results than Bardow's scheme with a same mesh size. Furthermore, the numerical stability of Bardow's 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 DUGKS is twice as expensive as the Bardow's scheme with the same mesh size. (C) 2016 Elsevier Inc. All rights reserved.
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