Publication Date

2006

Document Type

Thesis

Committee Members

Richard Bethke (Other), Bor Jang (Other), Joseph Slater (Advisor), Joseph Thomas (Other)

Degree Name

Master of Science in Engineering (MSEgr)

Abstract

Proper Orthogonal Decomposition (POD) provides a method of analyzing data and/or creating a Reduced Order Model (ROM). In this thesis, POD is used to create a ROM comprised of basis functions onto which the governing equations of a Computational Fluid Dynamics (CFD) problem are projected via Galerkin's method. The model is of reduced order since the basis functions span a space smaller than the space from which they were created. A full order simulation called the training period is conducted first to obtain data to be used for creating the ROM using POD. The dominant characteristics are extracted from the data using Karhunen- Loève analysis. Computational expense is recouped by applying the ROM to the original system with its design parameters varied from the training conditions. The influence of the individual POD basis functions on the solution varies. Additionally, changes to the design parameters and boundary conditions of the system may affect the influence of the individual basis functions. These basis functions can be ranked and the less influential basis functions can be truncated from the ROM, reducing computational expense. There are several methods that can be used to rank the basis functions. The work for this thesis seeks to find a way of determining the minimum amount of necessary modes needed to achieve an accurate solution. The methods used in this thesis are: tracking normalized error induced by exclusion of basis functions, the contribution of individual basis functions to the solution and the residual value of the excluded or truncated basis functions as proposed by Dr. Joseph Slater.

Page Count

105

Department or Program

Department of Mechanical and Materials Engineering

Year Degree Awarded

2006

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