On pressure and velocity boundary conditions for the lattice Boltzmann BGK model

TLDR

Boundary conditions for pressure/density and velocity in 2‑D and 3‑D lattice Boltzmann BGK models are a key challenge in computational fluid dynamics. The authors propose a new method to specify these boundary conditions. The method constructs conditions consistent with the wall boundary condition by applying bounceback of the non‑equilibrium distribution, using the incompressible LBGK model and half‑way wall bounceback for pressure inlet/outlet. Simulations recover the analytical plane Poiseuille flow solution, achieve approximately second‑order accuracy, and show error magnitudes comparable to other published boundary conditions while exhibiting better stability.

Abstract

Pressure (density) and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model [J. Stat. Phys. 81, 35 (1995)] the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure (density) difference. The half-way wall bounceback boundary condition is also used with the pressure (density) inlet/outlet conditions proposed in this paper and in Phys. Fluids 8, 2527 (1996) to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior.