Concept for a one-dimensional discrete artificial boundary condition for the lattice Boltzmann method

This article deals with artificial boundaries which you encounter when a large spatial domain is confined to a smaller computational domain. Such an artificial boundary condition should not preferably interact with the fluid at all. Standard boundary conditions, e.g., a pressure or velocity condition, result in unphysical reflections. So far, existing artificial boundary conditions for the lattice Boltzmann method (LBM) are transferred from macroscopic formulations. In this work we propose novel discrete artificial boundary conditions (ABCs) which are tailored on the LBM’s mesoscopic level. They are derived directly for the chosen LBM with the aim of higher accuracy. We describe the idea of discrete ABCs in a three velocity (D1Q3) model governing the Navier-Stokes equations in one dimension. We emphasize the fact that our approach has the approved potential to be generalized to higher dimensions and general collision models. Numerical results finally demonstrate the superiority of our new boundary condition in terms of accuracy compared to previously used ABCs.