重整化群理论在多孔介质upscale方法的统计比较中表现更优
Renormalization Group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media
AI总结：
本文通过统计研究，比较了多种upscale方法在多孔介质渗透率系数上的表现，发现基于Mode-Elimination重整化群理论的MG方法在精度和计算效率上均优于其他方法。
摘要：
确定多孔介质中实现预期流量所需的压差需要求解达西定律，一个类似拉普拉斯方程的方程，其空间变化的张量渗透率系数需要高空间分辨率采样。这使得数值求解达西方程变得计算上不可行。因此，许多努力集中在创建高分辨率有效模型上，以确保估计的流量率得到良好再现，从而凸显了计算成本与数值精度之间的经典权衡。本文通过统计研究，对大量超过渗透阈值的渗透率系数进行了比较，发现基于Mode-Elimination重整化群理论的MG方法在精度上更优，特别是因为它能够处理系数的张量性质。MG方法在我们实现的方式中具有较低的计算需求，并且在使用MG upscaled渗透率时，即使接近或超过渗透阈值，也能获得准确的流量率估计。
英文摘要：
Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a new technique based on Mode-Elimination Renormalization-Group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly so due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner that we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.
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