CMG: Renormalized Numerical Simulation (RNS) - Analytical, Computational and Statistical Tools for Modeling Complex Multiscale Flows in the Geosciences

该项目涉及一种新的方法来表示亚网格尺度的物理基础上的假设，即有未解决的尺度和最精细的尺度之间的自相似性解决。 计算几何技术将被用来表示在解析尺度中看到的结构;优化技术将被用来量化不同尺度下相似结构之间的关系;最后，自相似性将被用来将这些结构外推到未解析尺度。 开发的技术将通过将它们应用于两类动态模拟进行测试。 第一个是粗糙地形上的气流，第二个是复杂多孔介质中的地下水运移。 这项工作是在环境流体力学领域工作的数学家和科学家之间的合作。 它将为研究生提供跨学科的研究培训，将数学、计算科学和地球物理流体流动联系起来。

This project involves a novel approach to the representation of sub-grid scale physics based on the assumption that there is self-similarity between the unresolved scales and the finest scales resolved. Computational geometry techniques will be used to represent structures seen in the resolved scales; optimization techniques will be used to quantify the relation between similar structures at different scales; finally self-similarity will be used to extrapolate these structures to unresolved scales. The techniques developed will be tested by applying them to two classes of dynamical simulations. The first is airflow over rough terrain and the second is groundwater transport in complex porous media. The work is a collaboration between mathematicians and scientists working in the area of environmental fluid mechanics. It will offer interdisciplinary research training, bridging mathematics, computational science and geophysical fluid flow, to graduate students.