Modification of On-Site Velocity Boundary Condition in LBM for $$D_3Q_{27}$$ Lattice Structure

Abstract

In this paper, the on-site velocity boundary condition proposed by Zou and He (Phys Fluids 9(6):1591–1598, 1997) is modified for the $$D_3Q_{27}$$ lattice structure of the lattice Boltzmann method (LBM). The several benchmark case of fluid flow has been simulated to investigate the applicability of the proposed boundary condition. Firstly, incompressible laminar flow through a square duct has been chosen to investigate the accuracy and stability of the boundary condition. The derived boundary conditions have implemented at the inflow and outflow, and the simple bounce-back boundary condition has used to obtain the no-slip boundary condition at the walls of the square duct. The results are compared with the analytical solution of flow in an infinitely long rectangular duct. The accuracy and stability of the boundary condition have reported. Later, the modified boundary condition has implemented for the simulation of turbulent flow past a square cylinder confined in a rectangular duct. The simulation results are validated with the previous experimental data and numerical results reported in Kim et al. (Comput Fluids 33(1):81–96, 2004) and Nakagawa et al. (Exp Fluids 9(6):284–294, 1999).