Lattice Boltzmann method for antiplane shear deformation: non-lattice-conforming boundary conditions

Abstract In this work, two different approaches to treat boundary conditions in a lattice Boltzmann method (LBM) for the wave equation are presented. We interpret as governing of displacement field solid under simplified deformation assumptions, but algorithms not limited interpretation. A feature both is that does need conform with discretization, i.e., regular lattice. This allows larger flexibility regarding geometries can be handled by LBM. The first algorithm aims at determining missing distribution functions points such way desired macroscopic condition fulfilled. second only available Neumann-type and considers balance momentum control volumes on mesoscopic scale, scale spacing. Numerical examples demonstrate new indeed improve accuracy LBM compared previous results they able model complex do