Multilevel Upscaling in Heterogeneous Porous Media
D. Moulton, S. Knapek, Joel E. Dendy · 2004
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 upscaling methods do not balance these competing demands. In this paper we highlight a new efficient, numerical method, which combines our recent work on multigrid homogenization (MGH) [23, 25] with the work of Dvořak [14] 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. ∗This research was performed under the auspices of the U.S. Department of Energy, under contract W-7405-ENG-36, and is to be referenced as LA-UR 99-4754.