Asymptotic analysis of lattice boltzmann boundary conditions

In this article, we use a general method for the analysis of finite difference schemes to investigate lattice Boltzmann algorithms for Navier-Stokes problems with Dirichlet boundary conditions. Several link based boundary conditions for commonly used lattice Boltzmann BGK models are considered. With our method, the accuracy of the algorithms can be exactly predicted. Moreover, the analytical results can be used to construct new algorithms which is demonstrated with a corrected bounce back rule that requires only local evaluations but still yields second order accuracy for the velocity. The analysis is applicable to general geometries and instationary flows.