J. Moulton, S. Knapek, and J. Dendy.
Multilevel upscaling in heterogeneous porous media.
Technical report, CNLS Research highlight, Los Alamos Nat. Lab., Jan.
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The multiscale structure of heterogeneous porous media prevents a straightforward numerical treatment of the underlying mathematical flow models. In particular, fully resolved flow simulations are intractible and yet the fine-scale structure of a porous medium may significantly influence the coarse-scale properties of the solution (e.g., average flow rates). Consequently, homogenization or upscaling procedures are required to define approximate coarse-scale models suitable for efficient computation. Unfortunately, inherent in such a procedure is a compromise between its computational cost and the accuracy of the resulting coarse-scale solution. In general, most popular methods do not balance these competing demands. In this paper we highlight our new efficient, numerical method, which combines our recent work on multigrid homogenization (MGH) with the work of Dvorak to compute bounded estimates of the homogenized permeability for single phase saturated flows. Our approach is motivated by the observation that the coarse-scale influence of multiscale structures are captured automatically by robust variationally defined multigrid methods. The effectiveness of this new algorithm is demonstrated with numerical examples.