Curved Boundary Conditions for the Lattice Boltzmann Method

Abstract

The lattice Boltzmann method is a modern method in computational fluid dynamics. Its primary use is the simulation of incompressible flows. It has computational advantages over conventional methods like the finite volume method. However, the implementation of boundary conditions is still an unsolved topic for this method. The method is defined on a Cartesian grid such that curved walls need special treatment as they are generally not aligned with the grid lines. We investigated a number of straight and curved boundary conditions and performed four different benchmark tests to verify these. Based on a formulation for curved walls with no-slip from the literature, we showed that this method could be extended to simulate flows with arbitrary velocity boundary conditions. Our scheme conserved the second order accuracy of the lattice Boltzmann method in time and space.