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Talk Abstract
Nonlinear Subgrid Upscaling of Two-phase Flow in Porous Media

Todd Arbogast
Department of Mathematics
Center for Subsurface Modeling,
Texas Institute for Computational and Applied Mathematics
The University of Texas at Austin
Austin, Texas 78712 USA

We present an approach and numerical results for scaling up fine grid information to coarse scales in an approximation to a nonlinear parabolic system governing two-phase flow in porous media. The technique allows upscaling of the usual parameters porosity and relative and absolute permeabilities, and also the location of wells and capillary pressure. Some of these are critical nonlinear terms that need to be resolved on the fine scale, or serious errors will result. Upscaling is achieved by explicitly decomposing the differential system into a coarse-grid-scale operator coupled to a subgrid-scale operator. The subgrid-scale operator is approximated as an operator localized in space to a coarse-grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid-scale problems independently of the coarse-grid approximation. The coarse-grid problem is modified to take into account the subgrid-scale solution and solved as a large linear system of equations. Finally, the coarse scale solution is corrected on the subgrid-scale, providing a fine-grid scale representation of the solution. In this approach, no explicit macroscopic coefficients nor pseudo-functions result. The method is easily seen to be optimally convergent in the case of a single linear parabolic equation. Comptational results that illustrate and assess the technique are presented.

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