An accurate curved boundary treatment in the lattice Boltzmann method

The lattice Boltzmann equation (LBE) is an alternative kinetic method capab le of solving hydrodynamics for various systems. Major advantages of the me thod are due to the fact that the solution for the particle distribution fu nctions is explicit, easy to implement, and natural to parallelize. Because the method often uses uniform regular Cartesian lattices in space, curved boundaries are often approximated by a series of stairs that leads to reduc tion in computational accuracy. In this work, a second-order accurate treat ment of the boundary condition in the LEE method is developed for a curved boundary. The proposed treatment of the curved boundaries is an improvement of a scheme due to O. Filippova and D. Hanel (1998, J. Comput. Phys. 147, 219). The proposed treatment for curved boundaries is tested against severa l flow problems: 2-D channel flows with constant and oscillating pressure g radients for which analytic solutions are known, flow due to an impulsively started wall, lid-driven square cavity flow, and uniform flow over a colum n of circular cylinders. The second-order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes. The proposed boundary c ondition has well-behaved stability characteristics when the relaxation tim e is close to 1/2, the zero limit of viscosity. The improvement can make a substantial contribution toward simulating practical fluid flow problems us ing the lattice Boltzmann method. (C) 1999 Academic Press.