Abstract
The accuracy of the renormalization method for upscaling two-dimensional hydraulic conductivity fields is investigated, using two canonical 2 × 2 blocks: a checkerboard geometry and a geometry in which three of the cells have conductivity K 1 and the other has conductivity K 2. The predictions of the renormalization algorithm are compared to the arithmetic, harmonic and geometric means, as well as to theoretical predictions and finite element calculations. For the latter geometry renormalization works well over the entire range of the conductivity ratio K 2/K 1, but for the checkerboard geometry the error becomes unbounded as the conductivity ratio grows.
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Yeo, IW., Zimmerman, R.W. Accuracy of the Renormalization Method for Computing Effective Conductivities of Heterogeneous Media. Transport in Porous Media 45, 129–138 (2001). https://doi.org/10.1023/A:1011849804979
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DOI: https://doi.org/10.1023/A:1011849804979