A Non-uniform Staggered Cartesian Grid Approach for Lattice-Boltzmann Method

We propose a numerical approach based on the Lattice-Boltzmann method (LBM) for dealing with mesh refinement of Non-uniform Staggered Cartesian Grid. We explain, in detail, the strategy for mapping LBM over such geometries. The main benefit of this approach, compared to others, consists of solving all fluid units only once per time-step, and also reducing considerably the complexity of the communication and memory management between different refined levels. Also, it exhibits a better matching for parallel processors. To validate our method, we analyze several standard test scenarios, reaching satisfactory results with respect to other state-of-the-art methods. The performance evaluation proves that our approach not only exhibits a simpler and efficient scheme for dealing with mesh refinement, but also fast resolution, even in those scenarios where our approach needs to use a higher number of fluid units.