| Abstract: | The simulation of rarefied gas flows through complex porous media is challenging due to the tortuous flow pathways inherent to such structures. The Lattice
Boltzmann method (LBM) has been identified as a promising avenue to solve flows
through complex geometries due to the simplicity of its scheme and its high parallel
computational efficiency. It has been proposed to model the stress-strain relationship
with the extended Navier-Stokes equations rather than attempting to directly solve
the Boltzmann equation. However, a regularization technique is required to filter out
non-resolved higher-order components with a low-order velocity scheme. Although
slip boundary conditions (BCs) have been proposed for the non-regularized multiple
relaxation time LBM (MRT-LBM) for planar geometries, previous slip BCs have never
been verified extensively with the regularization technique. In this work, following
an extensive literature review on the imposition of slip BCs for rarefied flows with the
LBM, it is proven that earlier values for kinetic parameters developed to impose slip
BCs are inaccurate for the regularized MRT-LBM and differ between the D2Q9 and
D3Q15 schemes. The error was eliminated for planar flows and good agreement between analytical solutions for arrays of cylinders and spheres was found with a wide
range of Knudsen numbers. |
