We examine the validity of the commonly used Hagen-Poiseuille model of local resistance of porous media using direct numerical simulations. We provide theoretical arguments that highlight possible limitations of this model and formulate a new constitutive model that is based on the circularity of iso-pressure surfaces. We compare the performance of both models on three different three-dimensional artificial porous media. We show that the new model improves the root-mean-squared-relative error from , and for the HP model to , and for the three porous media respectively. We anticipate that our approach may find broad application in network models of porous media that are typically build from 3D images with intricate pore geometries.

中文翻译：

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非均质多孔介质中的局部水力阻力

我们使用直接数值模拟检验了常用的多孔介质局部阻力 Hagen-Poiseuille 模型的有效性。我们提供了强调该模型可能存在的局限性的理论论证，并制定了一个基于等压面圆度的新本构模型。我们比较了两种模型在三种不同的三维人造多孔介质上的性能。我们表明，该模型从提高根均方相对误差，并为HP模型，并分别对三个多孔介质。我们预计我们的方法可能会在多孔介质的网络模型中得到广泛应用，这些模型通常由具有复杂孔隙几何形状的 3D 图像构建而成。