Item – Theses Canada

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OCLC number
1017540763
Link(s) to full text
LAC copy
LAC copy
Author
Hemmings, Isabelle,1973-
Title
Eigensystem analysis of a numerical method for fluid dynamics.
Degree
M.A. Sc. -- University of Toronto, 1998
Publisher
Ottawa : National Library of Canada = Bibliothèque nationale du Canada, [1999]
Description
1 microfiche
Notes
Includes bibliographical references.
Abstract
Arnoldi's method was implemented to approximate the semi- and fully-discrete eigenvalues of ARC1D, a quasi-one-dimensional Euler solver. Three test cases were run to see the effects of different CFL numbers on the convergence rate and the approximations of the largest fully-discrete eigenvalue. Verification of the eigenvalue approximations was performed and an appropriate subspace size for Arnoldi's method was determined. A subspace size of about 40% of the original matrix size yields good results for the largest eigenvalues. The asymptotic convergence rate of the solver was found to agree closely with the largest eigenvalue of the fully-discrete operator matrix, confirming the linear behaviour of the operator. Similarly, a good correlation between the eigenvectors of the largest fully-discrete eigenvalues and the remaining error at a right-hand-side residual value of 10$\sp{-10}$ was found. Overall, these results indicate that, while Arnoldi's method is a very useful tool for obtaining the maximum eigenvalues of large matrices, it can require large subspace sizes which could be prohibitive in two and three dimensions.
ISBN
0612408973
9780612408975