Second order accurate boundary conditions for the general propagation lattice Boltzmann method

Abstract

In the present work, the problem of the development of the second order accurate boundary conditions for the lattice Boltzmann models with the general streaming step is addressed. The proposed boundary conditions are applicable to the flows in domains with solid and curved boundaries. The presented boundary scheme can be considered as the generalization of the Mei-Luo-Shyy conditions, in the case of the standard lattice Boltzmann models both approaches coincide. Several benchmark problems are considered: the Poiseuille flow, the oscillating Womersley flow, the Taylor-Couette flow, and the flow past a circular cylinder. These problems are studied for different spatial grid resolutions, and the convergence rates to the solutions from literature are presented.