Investigation of mesoscopic boundary conditions for lattice Boltzmann method in laminar flow problems

For use with the lattice Boltzmann method, the macroscopic boundary conditions need to be transformed into their mesoscopic counterparts. Commonly used mesoscopic boundary conditions use the equilibrium density function, which introduces undesirable artifacts into the numerical solution, especially near interfaces with other types of boundary conditions. In this work, several variants of the mesoscopic boundary conditions are summarized and numerically investigated by means of benchmark problems for the incompressible Navier-Stokes equations with known analytical solutions. To improve the numerical approximation of the velocity and pressure fields, moment-based boundary conditions are extended for the D3Q27 velocity model. Furthermore, the interpolated boundary conditions are improved. These newly developed boundary conditions are shown to produce results with a substantially smaller numerical error.