Multiscale Modeling and Simulation of Turbulent Geophysical Flows
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The accurate and efficient numerical simulation of geophysical flows is of great interest in numerical weather prediction and climate modeling as well as in numerous critical areas and industries, such as agriculture, construction, tourism, transportation, weather-related disaster management, and sustainable energy technologies. Oceanic and atmospheric flows display an enormous range of temporal and spatial scales, from seconds to decades and from centimeters to thousands of kilometers, respectively. Scale interactions, both spatial and temporal, are the dominant feature of all aspects of general circulation models in geophysical fluid dynamics. In this thesis, to decrease the cost for these geophysical flow computations, several types of multiscale methods were systematically developed and tested for a variety of physical settings including barotropic and stratified wind-driven large scale ocean circulation models, decaying and forced two-dimensional turbulence simulations, as well as several benchmark incompressible flow problems in two and three dimensions. The new models proposed here are based on two classes of modern multiscale methods: (i) interpolation based approaches in the context of the multigrid/multiresolution methodologies, and (ii) deconvolution based spatial filtering approaches in the context of large eddy simulation techniques. In the first case, we developed a coarse-grid projection method that uses simple interpolation schemes to go between the two components of the problem, in which the solution algorithms have different levels of complexity. In the second case, the use of approximate deconvolution closure modeling strategies was implemented for large eddy simulations of large-scale turbulent geophysical flows. The numerical assessment of these approaches showed that both the coarse-grid projection and approximate deconvolution methods could represent viable tools for computing more realistic turbulent geophysical flows that provide significant increases in accuracy and computational efficiency over conventional methods.
- Doctoral Dissertations