Dirichlet and Neumann boundary conditions for a lattice Boltzmann scheme for linear elastic solids on arbitrary domains

We propose novel, second-order accurate boundary formulations of Dirichlet and Neumann boundary conditions for arbitrary curved boundaries, within the scope of our recently introduced lattice Boltzmann method for linear elasticity. The proposed methodology systematically constructs and analyzes the boundary formulations on the basis of the asymptotic expansion technique; thus, it is expected to be of general applicability to boundary conditions for lattice Boltzmann formulations, well beyond the focus of this paper. For Dirichlet boundary conditions, a modified version of the bounce-back method is developed, whereas the Neumann boundary conditions are based on a novel generalized ansatz proposed in this work. The Neumann boundary formulation requires information from one additional neighbor node, for which a finite difference algorithm is introduced that enables the handling of very general boundary geometries. The theoretical derivations are verified by convergence studies using manufactured solutions, as well as by comparison with the analytical solution of the classical plate with hole problem.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).