Parallel Scheme for Multi-Layer Refinement Non-Uniform Grid Lattice Boltzmann Method Based on Load Balancing

The large-scale numerical simulation of complex flows has been an important research area in scientific and engineering computing. The lattice Boltzmann method (LBM) as a mesoscopic method for solving flow field problems has become a relatively new research direction in computational fluid dynamics. The multi-layer grid-refinement strategy deals with different-level of computing complexity through multi-scale grids, which can be used to solve the complex flow field of the non-uniform grid LBM without destroying the parallelism of the standard LBM. It also avoids the inefficiencies and waste of computational resources associated with standard LBMs using uniform and homogeneous Cartesian grids. This paper proposed a multi-layer grid-refinement strategy for LBM and implemented the corresponding parallel algorithm with load balancing. Taking a parallel scheme for two-dimensional non-uniform meshes as an example, this method presented the implementation details of the proposed parallel algorithm, including a partitioning scheme for evaluating the load in a one-dimensional direction and an interpolation scheme based on buffer optimization. Simply by expanding the necessary data transfer of distribution functions and macroscopic quantities for non-uniform grids in different parallel domains, our method could be used to conduct numerical simulations of the flow field problems with complex geometry and achieved good load-balancing results. Among them, the weak scalability performance could be as high as 88.90% in a 16-threaded environment, while the numerical simulation with a specific grid structure still had a parallel efficiency of 77.4% when the parallel domain was expanded to 16 threads