We present a new 3D lattice Boltzmann (LB) algorithm based on central moments for the D3Q27 lattice using a cuboid grid, which is parameterized by two grid aspect ratios that are related to the ratios of the particle speeds with respect to that along a reference coordinate direction. The use of the cuboid lattice grid enables the method to compute flows having different characteristic length scales in different directions more efficiently. It is constructed to simulate the Navier-Stokes equations consistently via introducing counteracting corrections to the second order moment equilibria obtained via a Chapman-Enskog analysis that eliminate the errors associated with the grid anisotropy and the non-Galilean invariant terms. The implementation is shown to be compact and modular, with an interpretation based on special matrices, admitting ready extension of the standard algorithm for the cubic lattice to the cuboid lattice via appropriate scaling of moments based on grid aspect ratios before and after collision step and equilibria corrections. The resulting formulation is general in that the same grid corrections developed for the D3Q27 lattice for recovering the correct viscous stress tensor is applicable for other lattice subsets, and a variety of collision models, including those based on the relaxation of raw moments, central moments and cumulants, as well as their special case involving the distribution functions. The cuboid central moment LBM is validated against a variety of benchmark flows, and when used in lieu of the corresponding raw moment formulation for simulating shear flows, we show that it results in significant improvements in numerical stability. Finally, we demonstrate that our cuboid LB approach is efficient in simulating anisotropic shear flow problems with significant savings in computational cost and memory storage when compared to that based on the cubic lattice.
翻译:我们展示了一个新的 3D lattice Boltzmann (LB) 算法, 以CABO 网格的中央时点为基础, 为D3Q27 Lattice 提供了一个新的 3D lattice Boltzmann (LB) 算法, 以 CABO 网格的中央时点为基础, 以 CABO 网格的中央时点为基础, 以 CCD3Q27 网格分析的方式, 消除与原始网格稳定性相关的错误和非伽利略的变异性关系网格比率。 使用 cUB 网格 网格, 使得能够按照不同方向计算不同特点长度的流量。 构建了Navier- Stokes 方格方程式, 通过对第二个时序进行校正校正, 通过 Chapman- Enskogy 分析, 消除了与原始网格 egroupol etpreal etrol 相联的差值相关的差数。 显示, 市级的市值的市值的市值的市值的市值流, 的市值和市值的市值的市值的市值的市值流, 的市值的市值的市值的市值的市值流, 的市值的市值的市值的市值的市值的市值的市值的市值, 、市值的市值流, 的市值的市值的市值的市值的市值的市值, 、市值的市值的市值的市值, 、市值的市值的市值的市值的市值的市值的市值的市值的市值的市值, 、市值的市值的市值、市值的市值的市值的流, 、市值、市值的市值的市值的市值的市值的市值的市值的市值、市值的市值的市值的市值的市值的市值的市值的市值的市值的市值的市值的市值的市值的流, 、市值的市值的市值之间的值的市值值的市值, 、市值值的