Abstract An efficient numerical scheme at the crossroad of Fourier based methods and boundary element methods is derived to upscale the permeability of porous media from Stokes flow within the pore space. The method relies on a variational framework which involves trial force fields and the Green function. The discretization of the trial force fields is carried out on a uniform grid, which allows for the use of fast Fourier transforms to evaluate the convolution product arising from the Green function. A discretization of the Green function consistent with the variational framework is introduced to ensure the upper bound status of the homogenized permeability. The energy consistent discretization is compared to six alternative discretizations arising from truncation of Fourier series or from various finite difference schemes, in terms of accuracy of the homogenized permeability and of the local velocity fields as well as on the number of iterations required for convergence of the iterative solver. The method is combined to a strategy to estimate the Representative Volume Element (RVE) size at a target accuracy level from a single simulation on a large sample to study the permeability and associated RVE size for the Voronoi cell model, over the whole range of porosity.

中文翻译：

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在均匀网格上离散化的多孔介质渗透率的基于 FFT 的有效放大，并估计 RVE 大小

摘要 在基于傅里叶的方法和边界元方法的交叉点上，推导出了一种有效的数值方案，以提高孔隙空间内斯托克斯流中多孔介质的渗透率。该方法依赖于涉及试力场和格林函数的变分框架。试验力场的离散化是在均匀网格上进行的，这允许使用快速傅立叶变换来评估由格林函数产生的卷积积。引入了与变分框架一致的格林函数的离散化，以确保均质渗透率的上限状态。能量一致离散化与由傅立叶级数截断或各种有限差分方案产生的六种替代离散化进行比较，在均质渗透率和局部速度场的准确性以及迭代求解器收敛所需的迭代次数方面。该方法与一种策略相结合，通过对大样本的单个模拟以目标精度水平估计代表性体积元素 (RVE) 大小，以研究整个孔隙度范围内 Voronoi 细胞模型的渗透率和相关 RVE 大小.