Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Slip flows in ducts are important numerous engineering applications, most notably microchannel flows. Compared to the standard no-slip Dirichlet condition, case of slip formulates as a Robin-type condition for fluid tangential velocity. Such an increase mathematical complexity is accompanied by more challenging numerical transcription. The present work concerns with this topic, addressing modeling velocity boundary lattice Boltzmann method (LBM) applied steady slow viscous inside nontrivial shapes. As novelty, we extend newly revised local second-order (LSOB) flow [Philos. Trans. R. Soc. A 378, 20190404 (2020)] implement within two-relaxation-time (TRT) framework. LSOB follows in-node philosophy where its operation principle seeks explicitly reconstruct unknown populations form third-order accurate Chapman–Enskog expansion, wall built-in normal Taylor-type condition. key point approach that required first- and momentum derivatives, rather than computed through nonlocal finite difference approximations, locally determined simple linear algebra procedure, whose formulation particularly aided TRT symmetry argument. To express obtained two approaches considered, called Lnode $$ \mathrm{Lnode} Lwall \mathrm{Lwall} , which operate node variables, respectively. These formulations developed prescribe physical over plane curved walls, including corners. Their consistency accuracy characteristics examined against alternative linkwise strategies impose velocity, such kinetic-based diffusive bounce-back scheme, central interpolation multireflection scheme. several schemes tested different 3D configurations, walls not conforming LBM uniform mesh. Numerical tests confirm advanced proposed revealing added challenge modeling, parabolic necessary requirement reach problem class.