Review of Upscaling Methods for Describing Unsaturated Flow

The representation of small-scale features can be a challenge when attempting to model unsaturated flow in large domains. Upscaling methods offer the possibility of reducing the amount of resolution required to adequately simulate such a problem. In this report, the various upscaling techniques that are discussed in the literature are reviewed. The following upscaling methods have been identified from the literature: (1) stochastic methods, (2) renormalization methods, and (3) volume averaging and homogenization methods; in addition, a final technique, full resolution numerical modeling, is also discussed. Each of these techniques has its advantages and disadvantages. The trade-off is a reduction in accuracy in favor of a method that is easier to employ. For practical applications, the most reasonable approach appears to be one in which any of the upscaling methods identified above maybe suitable for upscaling in regions where the variations in the parameter fields are small. For regions where the subsurface structure is more complex, only the homogenization and volume averaging methods are probably suitable. With the continual increases in computational capacity, fill-resolution numerical modeling may in many instances provide a tractable means of solving the flow problem in unsaturated systems.

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