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- W2073642714 abstract "We present a hierarchical transform that can be applied to Laplace-like differential equations such as Darcy's equation for single-phase flow in a porous medium. A finite-difference discretization scheme is used to set the equation in the form of an eigenvalue problem. Within the formalism suggested, the pressure field is decomposed into an average value and fluctuations of different kinds and at different scales. The application of the transform to the equation allows us to calculate the unknown pressure with a varying level of detail. A procedure is suggested to localize important features in the pressure field based only on the fine-scale permeability, and hence we develop a form of adaptive coarse graining. The formalism and method are described and demonstrated using two synthetic toy problems." @default.
- W2073642714 created "2016-06-24" @default.
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- W2073642714 date "2009-03-18" @default.
- W2073642714 modified "2023-10-18" @default.
- W2073642714 title "Hierarchical coarse-graining transform" @default.
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- W2073642714 doi "https://doi.org/10.1103/physreve.79.036704" @default.
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