Abstract Estimation of the permeability tensor is crucial for many natural and industrial porous media applications. Homogenization provides a rigorous framework to calculate effective parameters from pore-scale images of a representative unit cell of the porous medium by solving a boundary value problem, also known as closure problem, subject to global constraints. However, the latter are hard to satisfy for arbitrarily complex geometries. We have developed a novel computational algorithm to calculate rigorously the permeability tensor. The approach, here referred to as τ-SIMPLE, is based on introducing an artificial time scale τ to satisfy the global constraint within the SIMPLE iteration. We show that the proposed algorithm has high accuracy for both two-dimensional and three-dimensional periodically arranged geometries.

中文翻译：

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斯托克斯流均质化中封闭问题的τ-SIMPLE算法

摘要 渗透率张量的估计对于许多天然和工业多孔介质应用至关重要。均质化提供了一个严格的框架，通过求解受全局约束的边界值问题（也称为闭合问题），从多孔介质的代表性晶胞的孔隙尺度图像计算有效参数。然而，对于任意复杂的几何形状，后者很难满足。我们开发了一种新的计算算法来严格计算渗透率张量。该方法在此称为 τ-SIMPLE，它基于引入人工时间尺度 τ 来满足 SIMPLE 迭代中的全局约束。我们表明，所提出的算法对于二维和三维周期性排列的几何形状都具有很高的精度。