Wavelet-Galerkin Solution to the Water Hammer Equations
Publication: Journal of Hydraulic Engineering
Volume 135, Issue 4
Abstract
In this paper, a wavelet-Galerkin method is utilized to solve the hyperbolic partial differential equations describing transient flow in a simple pipeline. Two wavelets (Haar and Daubechies) are utilized as bases for the Galerkin scheme. The governing equations are solved for the expansion coefficients, which are then used to reconstruct the signal at the downstream end of the pipeline; the computed results are in an excellent agreement with those calculated by using the method of characteristics including laminar or linearized turbulent friction terms. Most importantly, the wavelet-Galerkin approach allows the transient flow equations to be solved directly for the expansion coefficients at a certain level of resolution. This can be used to form the wavelet multiresolution framework that can be utilized for further analysis, such as feature extraction and signal identification.
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© 2009 ASCE.
History
Received: Oct 2, 2006
Accepted: Oct 8, 2008
Published online: Apr 1, 2009
Published in print: Apr 2009
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