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.

Although there do exist a few aeroacoustic studies on harmful artificial phenomena related to the usage of non-uniform Cartesian grids in lattice Boltzmann methods (LBM), a thorough quantitative comparison between different categories of grid arrangement is still missing in the literature. In this paper, several established schemes for hierarchical grid refinement in lattice Boltzmann simulations are analyzed with respect to spurious aeroacoustic emissions using a weakly compressible model based on a D3Q19 athermal velocity set. In order to distinguish between various sources of spurious phenomena, we deploy both the classical Bhatnagar–Gross–Krook and other more recent collision models like the hybrid recursive-regularization operator, the latter of which is able to filter out detrimental non-hydrodynamic mode contributions, inherently present in the LBM dynamics. We show by means of various benchmark simulations that a cell-centered approach, either with a linear or uniform explosion procedure, as well as a vertex-centered direct-coupling method, proves to be the most suitable with regards to aeroacoustics, as they produce the least amount of spurious noise. Furthermore, it is demonstrated how simple modifications in the selection of distribution functions to be reconstructed during the communication step between fine and coarse grids affect spurious aeroacoustic artifacts in vertex-centered schemes and can thus be leveraged to positively influence stability and accuracy.