New Renormalization Schemes for Conductivity Upscaling in Heterogeneous Media

Two new renormalization schemes for conductivity upscaling in heterogeneous media are presented. The schemes follow previous ones by performing the renormalization over square cells of size 2d with d being the dimensionality. Contrasting with previous schemes, the two-dimensional scheme makes use of the exact 2 × 2 block-conductivity. On the basis of the structure of the exact two-dimensional block-conductivity, an analogous three-dimensional scheme is proposed. The new schemes are tested on a number of benchmark problems and are shown to be significantly more accurate than existing schemes.

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