One-point boundary condition for the lattice Boltzmann method

Abstract

We propose a correction to the bounce back boundary condition for lattice Boltzmann algorithms which improves the accuracy of pressure from zero to first order and the accuracy of velocity from first to second order. Compared to interpolation based corrections, our method has the advantage of being completely local. In fact, methods using interpolation face difficulties at boundary points where not enough neighboring nodes are available. We show that a combination with our method offers a natural solution to this problem.