Development and Application of Subgrid Upscaling

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The investigator considers a physical system representing a porousmedium, such as a groundwater aquifer or a petroleum reservoir. Themovement of, e.g., a contaminant or oil over several kilometers isstrongly influenced by the properties of the intervening rock. Whatappears to us to be bulk fluid flow is actually a complex process offluid flowing through high and low permeability regions. To simulatethe flow, one generally uses a coarse computational grid. In subgridupscaling, one incorporates fine-scale processes within the coarsegrid cells through a local and easily computed subgrid technique. Theprojects objective is to obtain provably improved accuracy andcomputational efficiency. Moreover, since this technique provides agood and easily computed approximation to the fine-scale movement ofthe fluids, the technique will be adapted so that the full fine-scaleproblem itself can be solved in significantly less time. One post-doc, two graduate students, and one undergraduate studentwill be involved in the research, and educated in theinterdisciplinary environment. The work will be disseminated atinterdisciplinary meetings and in the mathematics, groundwater, andreservoir simulation literature to maximize its impact.The contamination of groundwater is one of the most seriousenvironmental problems facing the nation. Improvements to thepredictive capabilities of groundwater simulations in heterogeneousformations would have a wide-ranging impact. The engineering ofpetroleum and natural gas production uses heavily subsurfacesimulation technologies as well. The subgrid upscaling method hasshown great promise, and this proposal will further its developmentwhile promoting important educational and societal objectives.