The traditional multi-level grid multiple-relaxation-time lattice Boltzmann method (MRT-LBM) requires interpolation calculations in time and space. It is a complex and computationally intensive process. By using the buffer technique, this paper proposes a new multi-level grid MRT-LBM which requires only spatial interpolation calculations. The proposed method uses a center point format to store multi-level grid information. The grid type determination in the flow field calculation domain is done using the axis aligned bounding box (AABB) triangle overlap test. According to the calculation characteristics of MRT-LBM, the buffer grid is proposed for the first time at the interface of different levels of grids, which is used to remove the temporal interpolation calculation and simplify the spatial interpolation calculation. The corresponding multi-level grid MRT-LBM algorithm is also presented for two-dimensional and three-dimensional flow field calculation problems. For the two-dimensional problem of flow around a circular cylinder, the simulation results show that a four-level grid MRT-LBM proposed in this paper can accurately obtain the aerodynamic coefficients and Strouhal number at different Reynolds numbers, and it has about 1/9 of the total number of grids as a single-level grid MRT-LBM and is 6.76 times faster. For the three-dimensional flow calculation problem, the numerical experiments of flow past a sphere are simulated to verify the numerical precision of the presented method at Reynolds numbers = 100, 200, 250, 300, and 1000. With the streamlines and velocity contours, it is demonstrated that the multi-level grid MRT-LBM can be calculated accurately even at the interface of different size grids.

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.