A general single-node second-order boundary condition for the lattice Boltzmann method

Abstract

In this work, we propose a general single-node nonslip hydrodynamic boundary condition for the lattice Boltzmann method. The construction of the boundary scheme is the combination of the bounce back rule for the nonequilibrium part of the density distribution and linear interpolation. The proposed boundary condition is very simple, universal, stable, and accurate. The asymptotic analysis of the newly proposed boundary condition confirms that is of second-order accuracy. The numerical experiments demonstrate that the boundary condition is indeed second-order accurate for both straight and curved boundaries.