This dissertation uses spatial filtering to develop a large eddy simulation reduced order model (LES-ROM) framework for fluid flows. Proper orthogonal decomposition is utilized to extract the dominant spatial structures of the system. Within the general LES-ROM framework, two approaches are proposed to address the celebrated ROM closure problem. No phenomenological arguments (e.g., of eddy viscosity type) are used to develop these new ROM closure models.
The first novel model is the approximate deconvolution ROM (AD-ROM), which uses methods from image processing and inverse problems to solve the ROM closure problem. The AD-ROM is investigated in the numerical simulation of a 3D flow past a circular cylinder at a Reynolds number $Re=1000$. The AD-ROM generates accurate results without any numerical dissipation mechanism. It also decreases the CPU time of the standard ROM by orders of magnitude.
The second new model is the calibrated-filtered ROM (CF-ROM), which is a data-driven ROM. The available full order model results are used offline in an optimization problem to calibrate the ROM subfilter-scale stress tensor. The resulting CF-ROM is tested numerically in the simulation of the 1D Burgers equation with a small diffusion parameter. The numerical results show that the CF-ROM is more efficient than and as accurate as state-of-the-art ROM closure models. / Ph. D. / Numerical simulation of complex fluid flows is often challenging in many realistic engineering, scientific, and medical applications. Indeed, an accurate numerical approximation of such flows generally requires millions and even billions of degrees of freedom. Furthermore, some design and control applications involve repeated numerical simulations for different parameter values. Reduced order models (ROMs) are an efficient approach to the numerical simulation of fluid flows, since they can reduce the computational time of a brute force computational approach by orders of magnitude while preserving key features of the flow.
Our main contribution to the field is the use of spatial filtering to develop better ROMs. To construct the new spatially filtered ROMs, we use ideas from image processing and inverse problems, as well as data-driven algorithms. The new ROMs are more accurate than standard ROMs in the numerical simulation of challenging three-dimensional flows past a circular cylinder.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/77626 |
| Date | 12 May 2017 |
| Creators | Xie, Xuping |
| Contributors | Mathematics, Iliescu, Traian, Borggaard, Jeffrey T., Gugercin, Serkan, Ross, Shane D. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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