Lattice Boltzmann methods for complex micro-flows: applicability and limitations for practical applications

The extensive evaluation studies of the lattice Boltzmann method for micro-scale flows (μ-flow LBM) by the author's group are summarized. For the two-dimensional test cases, force-driven Poiseuille flows, Couette flows, a combined nanochannel flow, and flows in a nanochannel with a square- or triangular cylinder are discussed. The three-dimensional (3D) test cases are nano-mesh flows and a flow between 3D bumpy walls. The reference data for the complex test flow geometries are from the molecular dynamics simulations of the Lennard-Jones fluid by the author's group. The focused flows are mainly in the slip and a part of the transitional flow regimes at Kn < 1. The evaluated schemes of the μ-flow LBMs are the lattice Bhatnagar–Gross–Krook and the multiple-relaxation time LBMs with several boundary conditions and discrete velocity models. The effects of the discrete velocity models, the wall boundary conditions, the near-wall correction models of the molecular mean free path and the regularization process are discussed to confirm the applicability and the limitations of the μ-flow LBMs for complex flow geometries. (invited review)