Abstract
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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Karim, M.R., Krabbenhoft, K. New Renormalization Schemes for Conductivity Upscaling in Heterogeneous Media. Transp Porous Med 85, 677–690 (2010). https://doi.org/10.1007/s11242-010-9585-9
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DOI: https://doi.org/10.1007/s11242-010-9585-9