论文标题
以对流为主的运输过去孤立无序的水槽：超越均质化
Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization
论文作者
论文摘要
我们研究了当对流在扩散上占主导地位时，溶质过去孤立的水槽的运输在界面域中，当水槽在空间中均匀分布时，评估了均化近似值的有效性。根据物理参数（假定较大的péclet号和damköhler号DA）和水槽的紧凑性，对此类近似值的校正可以是非本地，非平滑和非高斯人。在一个空间维度中，溶质分布开发了大型PE的楼梯结构，与传统时刻相比，用可信的间隔更好地描述了校正。在两个和三个维度中，溶质分布在每个水槽处几乎是单明的（并按水槽尺寸正规），但是由于合奏在可变的水槽位置上平均，它们的矩可以平滑。我们使用力矩扩张方法将校正近似于均化近似，从而通过其自由空间形式代替绿色的函数，并测试预测模拟的预测。我们显示，在两个或三个维度中，如何通过对DA的修饰变化随着水槽大小的变化而在均质的近似值中捕获疾病的前阶冲击。
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.
