Simplified lattice Boltzmann method on multi-resolution mesh

The simplified lattice Boltzmann method (SLBM), as a recent advancement in the lattice Boltzmann community, alleviates the intrinsic limitations of the standard lattice Boltzmann method by directly evolving macroscopic properties and nicely preserving numerical stability in high-Reynolds-number simulations. To enhance its capability of handling complex hydrodynamic/acoustic problems and to reduce computational efforts, an improved version of SLBM, which is applicable on multi-resolution mesh, is developed in this article. In this method, smooth transition of physical properties across the interface of meshes with different resolutions is ensured by a novel numerical strategy, which effectively couples the interpolation and the extrapolation algorithms. In the meantime, a rescaling algorithm is proposed to fix the inconsistency of time levels induced by the usage of multi-resolution mesh. Comprehensive evaluations of the accuracy, efficiency, and stability of the new method are carried out through benchmark tests of both hydrodynamic and acoustic problems.