Analysis of Hierarchical Grid Refinement Techniques for the Lattice Boltzmann Method by Numerical Experiments

Abstract

Over the last few decades, several grid coupling techniques for hierarchically refined Cartesian grids have been developed to provide the possibility of varying mesh resolution in lattice Boltzmann methods. The proposed schemes can be roughly categorized based on the individual grid transition interface layout they are adapted to, namely cell-vertex or cell-centered approaches, as well as a combination of both. It stands to reason that the specific properties of each of these grid-coupling algorithms influence the stability and accuracy of the numerical scheme. Consequently, this naturally leads to a curiosity regarding the extent to which this is the case. The present study compares three established grid-coupling techniques regarding their stability ranges by conducting a series of numerical experiments for a square duct flow, including various collision models. Furthermore the hybrid-recursive regularized collision model, originally introduced for cell-vertex algorithms with co-located coarse and fine grid nodes, has been adapted to cell-centered and combined methods.