An extrapolation method for boundary conditions in lattice Boltzmann method

A boundary treatment for curved walls in lattice Boltzmann method is proposed. The distribution function at a wall node who has a link across the physical boundary is decomposed into its equilibrium and nonequilibrium parts. The equilibrium part is then approximated with a fictitious one where the boundary condition is enforced, and the nonequilibrium part is approximated using a first-order extrapolation based on the nonequilibrium part of the distribution on the neighboring fluid node. Numerical results show that the present treatment is of second-order accuracy, and has well-behaved stability characteristics.