Reduced Order Modeling of Geophysical Flows Using Physics-Based and Data-Driven Modeling Techniques
Abstract
The growing advancements in computational power, algorithmic innovation, and the availability of data resources have started shaping the way we numerically model physical problems now and for years to come. Many of the physical phenomena, whether it be in natural sciences and engineering disciplines or social sciences, are described by a set of ordinary differential equations or partial differential equations which is referred as the mathematical model of a physical system. High-fidelity numerical simulations provide us valuable information about the flow behavior of the physical system by solving these sets of equations using suitable numerical schemes and modeling tools. However, despite the progress in software engineering and processor technologies, the computational burden of high-fidelity simulation is still a limiting factor for many practical problems in different research areas, specifically for the large-scale physical problems with high spatio-temporal variabilities such as atmospheric and geophysical flows. Therefore, the development of efficient and robust algorithms that aims at achieving the maximum attainable quality of numerical simulations with optimal computational costs has become an active research question in computational fluid dynamics community. As an alternative to existing techniques for computational cost reduction, reduced order modeling (ROM) strategies have been proven to be successful in reducing the computational costs significantly with little compromise in physical accuracy. In this thesis, we utilize the state of the art physics-based and data-driven modeling tools to develop efficient and improved ROM frameworks for large-scale geophysical flows by addressing the issues associated with conventional ROM approaches. We first develop an improved physics-based ROM framework by considering the analogy between dynamic eddy viscosity large eddy simulation (LES) model and truncated modal projection, then we present a hybrid modeling approach by combining projection based ROM and extreme learning machine (ELM) neural network, and finally, we devise a fully data-driven ROM framework utilizing long short-term memory (LSTM) recurrent neural network architecture. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. Throughout the thesis, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed ROM frameworks are robust and capable of predicting such fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.
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- OSU Theses [15752]