A Parallel Algorithm Based on Regularized Lattice Boltzmann Method for Multi-Layer Grids

Abstract

The regularized lattice Boltzmann method (RLBM) is an improvement of the lattice Boltzmann method (LBM). The advantage of RLBM is improved accuracy without increasing computational overheads. The paper introduces the method of multi-layer grids, the multi-layer grids have different resolutions which can accurately solve problems in computational fluid dynamics (CFD) without destroying the parallelism of RLBM. Simulating fluid flow usually requires a large number of grid simulations. Therefore, it is necessary to design a parallel algorithm for RLBM based on multi-layer grids. In this paper, a load-balancing-based grid dividing algorithm and an MPI-based parallel algorithm for RLBM on multi-layer grids are proposed. The load balancing-based grid dividing algorithm ensures that the workload is evenly distributed across processes, minimizing the discrepancies in computational load. The MPI-based parallel algorithm for RLBM on multi-layer grids ensures accurate and efficient numerical simulation. Numerical simulations have verified that the proposed algorithms exhibit excellent performance in both 2D and 3D experiments, maintaining high stability and accuracy. The multi-layer grids method is significantly better than single-layer grids in terms of CPU runtime and number of grids required. Comparative analysis with the OpenMP multi-threading method on the multi-layer grid RLBM shows that the proposed algorithm in this paper achieves superior speedup and efficiency.