Item – Theses Canada

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OCLC number
31778287
Author
Ghidaoui, Mohamed Salah,1964-
Title
Analysis of discretization strategies in fixed-grid method of characteristics solution in closed conduits.
Degree
Ph. D. -- University of Toronto, 1993
Publisher
Ottawa : National Library of Canada = Bibliothèque nationale du Canada, 1994.
Description
2 microfiches.
Notes
University Microfilms order no. UMI00459204.
Includes bibliographical references.
Abstract
A discretization problem arises whenever the fixed-grid method of characteristics is applied to a multiple pipe system or to systems in which the wavespeed is variable. Interpolation or wavespeed adjustment techniques are used as remedies. This thesis provides a comprehensive discussion of why the existing methods of analyzing the discretization errors are inadequate and why the existing interpolation strategies should only be applied cautiously, if at all. The primary objectives of this dissertation are to introduce qualitative, analytical and numerical approaches for evaluating various discretization strategies for the fixed-grid method of characteristics in closed conduits. More specifically, the qualitative study of the region of influence shows how discretization strategies distort the physical problem and alter the wavespeed. The analytical approach is based on developing the concept of an equivalent hyperbolic differential equation (EHDE) to study how discretization errors arise in pipeline applications for the most common interpolation techniques. In particular, it is shown that space-line interpolation and the Holly-Preissmann scheme are equivalent to a dissipative and dispersive wave model with an adjusted wavespeed, but that the latter method had additional source and sink terms. Further, time-line interpolation is shown to be equivalent to a superposition of two waves with different wavespeeds. In general, the EHDE concept evaluates the consistency of the numerical scheme, provides a mathematical description of the numerical dissipation and dispersion, gives an independent way of determining the Courant condition, allows the comparison of alternative approaches, finds the wave path and explains why higher order methods should usually be avoided. Finally, the numerical study of the discretization problem introduces the ratio of the total energy at time $t\ (E\sb{t})$ to the total energy at time zero $(E\sb0).$ The decay of this ratio is shown to be a natural measure of the numerical dissipation arising from the various interpolation approaches. This artificial dissipation does not arise in the wavespeed adjustment approach, as is shown theoretically and illustrated by example. This thesis also introduces a new method of transforming the partial differential equations of waterhammer into ordinary differential equations. In addition, a method of path independent integration is introduced and applied.
ISBN
0315862424
9780315862425