Development and Application of Subgrid Upscaling

研究者认为一个物理系统代表一个多孔介质，如地下水含水层或石油储层。 例如，几公里范围内的污染物或石油受到中间岩石性质的强烈影响。 在我们看来，流体的整体流动实际上是一个复杂的过程，流体流过高渗透率和低渗透率区域。 为了模拟流动，一般使用粗糙的计算网格。 在subgridupscaling，一个包含在coarsegrid细胞通过本地和易于计算的子网格技术的精细尺度的过程。 该项目的目标是获得可证明的提高精度和计算效率。 此外，由于这种技术提供了一个很好的和容易计算的近似精细尺度运动的流体，该技术将适应，使整个精细尺度问题本身可以解决在显着更少的时间。一名博士后，两名研究生和一名本科生将参与研究，并在跨学科的环境中接受教育。 这项工作将在跨学科会议和数学、地下水和水库模拟文献中传播，以最大限度地发挥其影响。地下水污染是国家面临的最严重的环境问题之一。 提高非均质地层中地下水模拟的预测能力将产生广泛的影响。 石油和天然气生产工程也大量使用地下模拟技术。 亚网格尺度放大方法已经显示出巨大的前景，这一建议将进一步发展，同时促进重要的教育和社会目标。

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.