Boundary conditions for lattice Boltzmann simulations with complex geometry flows

Boundary conditions of lattice Boltzmann method to simulate flows embedded with a solid object is proposed. The closest nodes adjacent to the boundary in the fluid domain are used as boundary nodes of the flow domain. The fluid velocity of the boundary node is obtained by linear interpolation between the velocities of the solid object and the second fluid node further away. Then, distribution functions originating from the solid domain at the boundary nodes are modified using known distribution functions and correctors to satisfy the momentum. This boundary condition is an extended form of a method proposed by Hou et al. [C.F. Hou, C. Chang, C.A. Lin, Consistent boundary conditions for 2D and 3D Lattice Boltzmann simulations (submitted for publication)] for plane wall and regular geometry. The technique is examined by simulating decaying vortex, transient flow induced by an abruptly rotating ring and flow over an asymmetrically placed cylinder. Numerical simulations indicate that this method is second order accurate, and all the numerical results are compatible with the benchmark solutions.