We propose two postprocessing procedures (Patch method and Stitch method) to recover local conservation of velocity fields produced by multiscale approximations that are only conservative in coarse scales. These procedures operate on small overlapping regions and are designed to be implemented in parallel, which makes them relatively inexpensive. We investigate the applicability of such methods when tested on single-phase flow problems using the Multiscale Robin Coupled Method (MRCM) in highly heterogeneous permeability fields for modeling the contaminant transport in the subsurface. Numerical simulations are presented aiming to illustrate and compare the performance of the new methods with a standard procedure, the Mean method, in terms of accuracy in contaminant concentration. We show that for a collection of permeability fields taken as log-normal fields, the new postprocessing procedures provide similar or better accuracy than the Mean method. Then, we turn our attention to flows in high-contrast channelized porous formations, where the new methods robustly yield more accurate results and should thus be favored.

中文翻译：

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多尺度混合方法的速度后处理方案，应用于地下流中的污染物传输

我们提出了两种后处理程序（Patch方法和Stitch方法），以恢复由多尺度近似（仅在粗尺度上是保守的）产生的速度场的局部守恒。这些过程在较小的重叠区域上运行，并且设计为并行执行，这使得它们相对便宜。我们使用多尺度罗宾耦合法（MRCM）在高度非均质渗透率领域中对地下污染物传输建模的单相流问题测试中，研究了此类方法的适用性。数值模拟旨在说明和比较新方法与标准方法均值的性能。污染物浓度的准确性方面的方法。我们表明，对于作为对数正态场使用的渗透率场的集合，新的后处理程序提供的方法与均值方法相似或更好。然后，我们将注意力转向高对比度通道化多孔地层中的流动，在那里新方法可以稳健地产生更准确的结果，因此应受到青睐。