Analysis of lattice Boltzmann boundary conditions

Abstract

The correct implementation of Navier‐Stokes boundary conditions in the framework of lattice Boltzmann schemes is complicated by the non‐availability of analytical methods to assess the consistency of such discretizations. To close this gap, we propose a simple direct asymptotic analysis which is readily applicable to finite difference discretizations of initial boundary value problems in general and to lattice Boltzmann methods in particular. Results of the analysis applied to the classical lattice Boltzmann scheme with bounce back boundary condition are reported.