Kinetic Slip Boundary Condition for Isothermal Rarefied Gas Flows Through Static Non-Planar Geometries Based on the Regularized Lattice-Boltzmann Method (Communications in Computational Physics, 2022)
The simulation of rarefied gas flows through complex porous media is challenging due to the tortuous flow pathways inherent to such structures. The LatticeBoltzmann method (LBM) has been identified as a promising avenue to solve flowsthrough complex geometries due to the simplicity of its scheme and its high parallelcomputational efficiency. It has been proposed to model the stress-strain relationshipwith the extended Navier-Stokes equations rather than attempting to directly solvethe Boltzmann equation. However, a regularization technique is required to filter outnon-resolved higher-order components with a low-order velocity scheme. Althoughslip boundary conditions (BCs) have been proposed for the non-regularized multiplerelaxation time LBM (MRT-LBM) for planar geometries, previous slip BCs have neverbeen verified extensively with the regularization technique. In this work, followingan extensive literature review on the imposition of slip BCs for rarefied flows with theLBM, it is proven that earlier values for kinetic parameters developed to impose slipBCs are inaccurate for the regularized MRT-LBM and differ between the D2Q9 andD3Q15 schemes. The error was eliminated for planar flows and good agreement between analytical solutions for arrays of cylinders and spheres was found with a widerange of Knudsen numbers.