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

TL;DR

This paper develops and validates new pressure and velocity boundary conditions for 2D and 3D lattice Boltzmann BGK models, achieving high accuracy and compatibility with improved models for fluid flow simulations.

Contribution

It introduces a novel method for specifying boundary conditions that are consistent with previous bounce-back ideas and demonstrates their second-order accuracy and effectiveness.

Findings

Boundary conditions are second-order accurate.

Results recover analytical solutions with machine precision.

Compatible with improved incompressible LBGK models.

Abstract

Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and new method to specify these conditions are proposed. These conditions are consistent with the boundary condition we proposed in a previous paper using an idea of bounce-back of non-equilibrium distribution. These conditions give excellent results for the regular LBGK models, and were shown to be second-order accurate by numerical examples. When they are used together with the improved incompressible LBGK model proposed by zou et al. the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy.