An accurate curved boundary treatment in the lattice Boltzmann method

The lattice Boltzmann equation (LBE) is an alternative kinetic method capable of solving various hydrodynamics problems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and natural to parallelize. Because the method often uses uniform regular Cartesian lattices in space, curved boundaries are typically approximated by a series of stairs that leads to reduction in computational accuracy. In this work, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary, which is an improvement of a scheme due to Filippova & Hänel [J. Comp. Phys. 143, 426 (1998)]. The proposed treatment for curved boundaries is tested against several flow problems: 2-D channel flows with constant and oscillating pressure gradients for which analytic solutions are known, flow due to an impulsively started wall, lid-driven square cavity flow, and uniform flow over a column of circular cylinders. The second-order accuracy is observed with solid boundary arbitrarily placed between lattice nodes. The proposed boundary condition has well behaved stability characteristics when the relaxation time is close to Vi, the zero limit of viscosity. The improvement can make a substantial contribution toward simulating practical fluid flow, problems using the lattice Boltzmann method.