The effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows by Lattice-Boltzmann method

Abstract

The aim of this study is to investigate the effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows in the context of single relaxation time Lattice Boltzmann method (SRT-LBM). The fluid flows are simulated using regularized, no-slip, Zou-He and bounce back boundary conditions for straight surfaces in a lid driven cavity and the two-dimensional flow in a channel. The solutions for all types of the boundary conditions show good agreement with numerical references and exact solutions. The cavity pressure contours at low relaxation time show drastic perturbations for Zou-He boundary condition, whereas, the perturbation is ignorable for regularized boundary condition. At High Reynolds number, severe velocity gradients are major reason for numerical instabilities. Therefore, regularized boundary condition, which considers the velocity gradient in its calculation, has better numerical stability comparing the Zou-He boundary condition. Overall, the selection of appropriate boundary condition depends on the flow regime and Geometry. The proper boundary conditions at low Reynolds numbers are Zou-He and bounce back boundary conditions, and at high Reynolds numbers, regularized and no-slip boundary conditions are recommended.