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首页> 外文期刊>Journal of Computational Physics >Error analysis and correction for Lattice Boltzmann simulated flow conductance in capillaries of different shapes and alignments
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Error analysis and correction for Lattice Boltzmann simulated flow conductance in capillaries of different shapes and alignments

机译：格子和玻尔兹曼模拟的不同形状和排列的毛细管中的流导的误差分析和校正

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摘要

We study the relative error in conductance calculations, for simulated flow of a single component single phase fluid through a capillary in three dimensions, by the Lattice Boltzmann (LB) method with bounce-back boundary conditions. The relative error with respect to analytical results for capillary cross-sections of circular, triangular and square shapes are calculated as a function of the cross-section diameter, a, and for different alignment of the cross-section relative to the underlying lattice grid. It is shown, when the shapes are not aligned perfectly to the lattice, that the relative error decreases systematically with the size, a, as ～1/a when a is evaluated by mapping the computed cross-sectional area, in terms of the enclosed number of grid points, to the respective geometrical shapes concerned. For perfectly aligned geometries, viz. the square capillary aligned to the LB lattice grid or rotated with its side along the diagonal of the LB grid, the relative error decreases as ～1/a ~2. A simple method is suggested to locate the boundary wall depending on its orientation relative to the grid, such that the exact conductance of the new shape matches the LB computed conductance.
机译：我们通过具有反弹边界条件的Lattice Boltzmann（LB）方法研究电导计算的相对误差，以模拟单组分单相流体通过毛细管在三个维度上的流动。关于圆形，三角形和正方形的毛细管横截面的分析结果的相对误差是根据横截面直径α和横截面相对于下面的格子网格的不同对准来计算的。结果表明，当形状未完全对准晶格时，相对误差随着尺寸a的减小而系统地减小，当a通过对计算出的横截面积进行映射来评估a时，相对误差为〜1 / a网格点的数量，取决于相关的几何形状。对于完美对齐的几何，即。方形毛细管与LB网格对齐或沿LB网格的对角线旋转时，相对误差减小约〜1 / a〜2。建议使用一种简单的方法根据边界壁相对于网格的方向进行定位，以使新形状的精确电导与LB计算的电导相匹配。

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