Automatic grid refinement criterion for lattice Boltzmann method

In all kinds of engineering problems, and in particular in methods for computational fluid dynamics based on regular grids, local grid refinement is of crucial importance. To save on computational expense, many applications require to resolve a wide range of scales present in a numerical simulation by locally adding more mesh points. In general, the need for a higher (or a lower) resolution is not known a priori, and it is therefore difficult to locate areas for which local grid refinement is required. In this paper, we propose a novel algorithm for the lattice Boltzmann method, based on physical concepts, to automatically construct a pattern of local refinement. We apply the idea to the two-dimensional lid-driven cavity and show that the automatically refined grid can lead to results of equal quality with less grid points, thus sparing computational resources and time. The proposed automatic grid refinement strategy has been implemented in the parallel open-source library Palabos.