Item – Theses Canada

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OCLC number
28216081
Author
Ghidaoui, Mohamed Salah,1964-
Title
Accuracy, stability and development of water hammer equations.
Degree
M.A. Sc. -- University of Toronto, 1991
Publisher
Ottawa : National Library of Canada = Bibliothèque nationale du Canada, 1991.
Description
2 microfiches.
Notes
University Microfilms order no. UMI00298272.
Includes bibliographical references.
Abstract
One of the purposes of this thesis is to provide a comprehensive discussion of the numerical errors associated with the physical modelling of unsteady fluid flow in closed conduits. There are two primary problems relating to the numerical solution of the unsteady flow equations: (1) the friction term is non-linear and cannot be integrated analytically, introducing a truncation error $E\sb{t}$, where t is the upper limit of integration; (2) the truncation error $E\sb{t}$ introduced into the state vector (Q(t), H(t)) will propagate and produce mathematical distortion at future states. In the typical method of characteristic solutions to the governing water hammer conditions in closed conduits, analytic integration of the compatibility equation along its characteristics is not possible because the variation of flow along this path is not known. To avoid this problem, this thesis introduces an iterative method of integration based on Picard's theorem. The result is a sequence of progressively better approximations that is guaranteed to converge uniformly to the exact solution as the number of terms in the series is increased. This thesis introduces new and simpler methods of establishing the second stability criterion for the various friction approximations. In addition, a sufficient condition for stability has been developed. (Abstract shortened by UMI.)
ISBN
0315654287
9780315654280