Permeability and effective dispersion tensors are critical parameters to characterize flow and transport in porous media at the continuum scale. Homogenization theory defines a framework in which such effective properties are first computed from solving a closure problem in a repeating unit cell of the periodic microstructure and then used in a macroscopic formulation for efficient computation. The closure problem is formulated as a local boundary value problem subjected to global constraints, which guarantee the uniqueness of the solution and can be difficult to satisfy for complex geometries and at high flow conditions. These constraints also ensure that pore-scale pressure, velocity, and concentration fields can be accurately reconstructed from the closure variable. Building on previous work, here we present a framework that allows to satisfy global constraints associated to both the permeability and the dispersion closure problems by introducing two artificial time scales. The algorithm, called -SIMPLE, computes both permeability and effective dispersion given an arbitrarily complex geometry and flow condition. This algorithm is demonstrated to be accurate for both 2D and 3D geometries across varying flow conditions, and thus it can be used to quickly characterize effective properties from porous media images in many applications.

中文翻译：

---

对色散闭合问题实施全局约束：[公式省略]-SIMPLE算法


渗透率和有效色散张量是在连续介质尺度上表征多孔介质流动和传输的关键参数。均质化理论定义了一个框架，在该框架中，首先通过解决周期性微观结构的重复晶胞中的闭合问题来计算此类有效属性，然后将其用于宏观公式中以进行有效计算。闭合问题被表述为受全局约束的局部边值问题，这保证了解的唯一性，并且对于复杂的几何形状和高流量条件来说很难满足。这些约束还确保可以根据闭合变量准确地重建孔隙尺度压力、速度和浓度场。基于之前的工作，我们在这里提出了一个框架，通过引入两个人工时间尺度，可以满足与渗透率和色散闭合问题相关的全局约束。该算法称为 -SIMPLE，在给定任意复杂的几何形状和流动条件的情况下计算渗透率和有效扩散。该算法被证明对于不同流动条件下的 2D 和 3D 几何形状都是准确的，因此可用于在许多应用中快速表征多孔介质图像的有效属性。