Comparative study of the lattice Boltzmann collision models for simulation of incompressible fluid flows

Abstract

In this paper, several lattice Boltzmann (LB) collision models are evaluated by a comparative study for simulation of incompressible fluid flows with periodic and also with curved wall boundaries. Herein, the single-relaxation-time (SRT) scheme based on the Bhatnagar–Gross–Krook (BGK) approximation, multiple-relaxation-time (MRT), regularized lattice Boltzmann (RLB) and the entropic lattice Boltzmann (ELB) methods are considered. The doubly periodic shear layers flow problem is computed in two different Reynolds numbers to investigate the robustness and performance of the collision operators applied. Efficiency and accuracy of these techniques are also examined by computing the incompressible fluid flows around a circular cylinder at various flow conditions. The predicted results are compared with the experiments and the numerical results performed by other researchers. The present study demonstrates that the SRT model is accurate enough and efficient for simulation of fluid flows with low Reynolds numbers. This scheme, however, suffers from numerical instabilities at moderate Reynolds numbers and requires very fine grid resolutions to remain stable. It is found that the ELB scheme does not sufficiently reduce the numerical oscillation at high Reynolds number flows. This method provides fewer stability benefits while being more computationally expensive. The results obtained show that the MRT and RLB models are stable (in contrast to SRT and ELB) for all the cases considered in the present work even at high Reynolds numbers. In terms of computational efficiency and accuracy, the MRT and RLB schemes are more attractive and provide the results comparable to those of other experimental and numerical methods. The present study suggests that these two techniques based on the implementation of the lattice Boltzmann method are robust, sufficiently accurate and computationally efficient to resolve the flow structures and properties around the practical geometries even at high Reynolds numbers.