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

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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.