基于非结构化网格的高可扩展并行有限体积格子Boltzmann方法

Scalable Parallel Finite Volume Lattice Boltzmann Method Based on Unstructured Grid

均匀网格格子Boltzmann方法虽然有其优势,但是在模拟大规模流场信息以及复杂几何边界时仍然存在困难。为此,文中给出了非结构化网格下的有限体积格子Boltzmann方法。该方法采用cell-centered方案,使用low-diffusion Roe方案计算对流通量密度,通过最小二乘方法计算粒子分布函数的梯度。为了能够模拟大规模复杂流场情况,文中给出了非结构化网格有限体积格子Boltzmann方法的并行方法。该法通过ParMETIS划分流场的非结构化网格,将网格近似平均地发送给MPI进程,比较了两种不同规模的网格单元的并行性能。文中通过以下两点验证了并行算法的正确性:1)顶盖方腔驱动流,Re=400,1 000,3 200,5 000;2)圆柱绕流,Re=10,20,40。并行数值实验的结果表明所提并行算法在1 920核上仍然拥有良好的可扩展性,在1 920个核上的并行效率可以达到在240核上效率的78.42%。

Although the lattice Boltzmann method(LBM)has become an effective and promising approach in computational fluid dynamics(CFD),it is still difficult to simulate large-scale flow field with complex geometric boundaries.In this paper,the finite volume lattice Boltzmann method with cell-centered scheme on unstructured grids was given.The convective fluxes are evaluated by low-diffusion Roe scheme,and the gradients of the particle distribution function are computed with Green-Gauss approach.In order to simulate large-scale complex flow field,a parallel algorithm for the finite volume lattice Boltzmann method on unstructured grids was presented.In this method,ParMETIS is applied to partition the unstructured mesh,and then the partitioned meshes are sent to the MPI processes.The parallel performance of two kinds of meshes are compared.The correctness of the parallel algorithm was verified by two benchmark flows:1)the lid-driven flow with Re=400,1 000,3 200,5 000;2)the steady viscous flow past a circular cylinder with Re=10,20,40.The results of parallel numerical experiments show that the parallel algorithm still has good scalability on 1 920 cores,which achieves 78.42%efficiency on 1 920 cores compared with 240 cores.