Multi-scale Models for Geophysical and Astrophysical Flows
Michael Calkins
Applied Mathematics,Ìý
Date and time:Â
Tuesday, November 18, 2014 - 12:00pm
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ECCR 257
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Fluid systems are ubiquitous features of the universe. Most of the planets within our Solar System are enveloped in a gaseous atmosphere and contain liquid metal cores at depth. The dynamical processes within these fluid volumes often control the temporal evolution of these bodies by, for example, controlling the amount of heat that escapes outwards to space. Although the equations that model fluid flow have been known for over a century, the disparate spatiotemporal scales that characterize the dynamics of natural fluid systems results in equations that are too numerically stiff to solve at realistic parameters. Even with the use of efficient numerical techniques and massively-parallel computing architectures, this difficulty will likely remain through the end of this century. One approach for overcoming this issue is to exploit the scale disparity inherent to these systems by employing multi-scale modeling strategies. In many cases this approach can be done in a mathematically rigorous manner with the use of multi-scale asymptotics that relies on dominant balances in the governing equations and spatial anisotropy in the dynamics. The resulting models possess many computational advantages, and provide a more transparent view of the physics when compared to the full, unapproximated set of governing equations. I'll describe how we have been using this approach for developing more realistic models of buoyancy-driven turbulence and planetary dynamos, the computational techniques that we employ, and outline approaches for other problems of interest.