Accurate imposition of boundary conditions (BCs) is of critical importance in fluid flow computation. This is especially true for the Lattice Boltzmann method (LBM), where BC imposition is done through operations on populations rather than directly on macroscopic variables. While the regular Cartesian structure of the lattices is an advantage for flow simulation through complex geometries such as porous media, imposition of correct BCs remains a topic of investigation for rarefied flows, where slip BCs need to be imposed. In this work, current kinetic BCs from the literature are reviewed for rarefied flows and an extended version of a technique that combines bounce-back and diffusive reflection (DBB BC) is proposed to solve such flows that exhibit effective viscosity gradients. The extended DBB BC is completely local and addresses ambiguities as regards to the definition of boundary populations in complex geometries. Numerical tests of a rarefied flow through a slit were performed, confirming the intrinsic second-order convergence of the proposed extended DBB BC. It settles a long-standing debate regarding the convergence of BCs in rarefied flows. Good agreement was also found with existing numerical schemes and experimental data.
A Lattice Boltzmann Method for relativistic rarefied flows in (2+1) dimensions