A consistent hydrodynamic boundary condition for the lattice Boltzmann method

Abstract

A hydrodynamicboundary condition is developed to replace the heuristic bounce‐back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two‐dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce‐back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamicboundary conditions, the lattice Boltzmann method is shown to exhibit second‐order accuracy.