On pressure and corner boundary conditions with two lattice Boltzmann construction approaches

A pressure (density) and a corner no‐slip boundary condition formulation are introduced for the two‐dimensional lattice Boltzmann method and numerically tested for the Hagen–Poiseuille flow case in this work. Both formulations are derived independently of the equilibrium distribution function model and no bounce‐back rule is needed. The corners are free of interpolations and are implemented with collisions. The Hermite‐based and the ‘entropy’‐based lattice Boltzmann constructions are reviewed, described in some details and compared. The best two models from each approach are chosen. An indirect substitution of the boundary values in the equilibrium distribution function is further expanded to its ‘entropic’ counterpart. For the straight walls, two existing boundary conditions with first and second order of accuracy are selected. The numerical results demonstrate that the presented boundary conditions are capable to preserve up to the second order of accuracy, depending on the straight walls. Based on the theoretical and numerical results, the so called Hermite construction is the recommended approach for isothermal incompressible flows.