Implementation of D3Q19 Lattice Boltzmann Method with a Curved Wall Boundary Condition for Simulation of Practical Flow Problems

In this paper, implementation of an extended form of a no-slip wall boundary condition is presented for the three-dimensional (3-D) lattice Boltzmann method (LBM) for solving the incompressible fluid flows with complex geometries. The boundary condition is based on the off-lattice scheme with a polynomial interpolation which is used to reconstruct the curved or irregular wall boundary on the neighboring lattice nodes. This treatment improves the computational efficiency of the solution algorithm to handle complex geometries and provides much better accuracy comparing with the staircase approximation of bounce-back method. The efficiency and accuracy of the numerical approach presented are examined by computing the fluid flows around the geometries with curved or irregular walls. Three test cases considered herein for validating the present computations are the flow calculation around the NACA0012 wing section and through the two different porous media in various flow conditions. The study shows the present computational technique based on the implementation of the three-dimensional Lattice Boltzmann method with the employed curved wall boundary condition is robust and efficient for solving laminar flows with practical geometries and also accurate enough to predict the flow properties used for engineering designs.