通过孤立无序汇的平流主导输送：超越均匀化
Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization
摘要：
我们调查的溶质运输过去孤立的汇在有界的域时，平流是占主导地位的扩散，评估均匀化近似的有效性时，汇均匀随机分布在空间中。对这种近似的修正可以是非局部的、非光滑的和非高斯的，这取决于物理参数（假设Péclet数Pe很大，Damköhler数Da）和汇的紧凑性。在一个空间维度上，溶质分布发展的阶梯结构大Pe，更好地描述与可信的间隔比传统的时刻与校正。在二维和三维，溶质分布是近奇异的在每个水槽（和正规化的水槽大小），但他们的时刻可以作为一个结果，在可变的水槽位置的集合平均平滑。我们近似修正的均匀化近似使用的时刻膨胀法，取代其自由空间形式的格林函数，并测试预测模拟。我们展示了如何，在两个或三个维度上，无序的领先顺序的影响，可以捕获在一个均匀化近似的合奏平均浓度，通过修改Da的增长与减小的水槽大小。
英文摘要：
We investigate the transport of a solute past isolated sinks in a bounded domain when advection is dominant over diffusion, evaluating the effectiveness of homogenization approximations when sinks are distributed uniformly randomly in space. Corrections to such approximations can be non-local, non-smooth and non-Gaussian, depending on the physical parameters (a Péclet number Pe, assumed large, and a Damköhler number Da) and the compactness of the sinks. In one spatial dimension, solute distributions develop a staircase structure for large Pe, with corrections being better described with credible intervals than with traditional moments. In two and three dimensions, solute distributions are near-singular at each sink (and regularized by sink size), but their moments can be smooth as a result of ensemble averaging over variable sink locations. We approximate corrections to a homogenization approximation using a moment-expansion method, replacing the Green's function by its free-space form, and test predictions against simulation. We show how, in two or three dimensions, the leading-order impact of disorder can be captured in a homogenization approximation for the ensemble mean concentration through a modification to Da that grows with diminishing sink size.
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