Across a wide range of flows, to date the Spatial Markov Model, a member of the continuous time random walk family of models, has had great success in predicting mean transport behavior - e.g. breakthrough curves and the temporal scaling of flow aligned spatial moments, but applications to modeling mixing and reactions have been more limited. This is because these are nonlinear in nature, whereby simply predicting mean behavior is not sufficient to reproduce large scale behaviors. Any model that aims to capture these must account for subscale fluctuations. We propose a series of novel approaches, which mix up and downscaling methods, to enable this. We start with a simple periodic system where we can rigorously explain our approach and then extend it to more complex realistic porous media, showing that they can have equal success there.
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