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Type: Conference paper
Title: Von Neumann stability analysis of a method of characteristics visco-elastic pipeline model
Author: Zecchin, A.
Simpson, A.
Lambert, M.
Citation: Papers presented at : 10th International Conference on Pressure Surges : Edinburgh, UK, 14-16 May 2008 / [S. Hunt, ed.] : pp.333-347
Publisher: BHR Group
Publisher Place: CD
Issue Date: 2008
ISBN: 9781855980952
Conference Name: International Conference on Pressure Surges (10th : 2008 : Edinburgh)
Statement of
A. C. Zecchin, A. R. Simpson, M. F. Lambert
Abstract: In recent years, investigation into the transient behaviour of viscoelastic pipelines has become a focus of modelling real world systems. For a pipeline made of viscoelastic material, the circumferential stress-strain relationship of the pipe is expressed as a convolution of the pressure history with the materials creep-compliance curve in the mass continuity equation. The creep compliance curve is typically approximated by a finite number of Kelvin-Voigt models in series, each parameterised differently. This model structure lends itself to a recurrence type relationship when implemented in a method of characteristics discretised scheme. The stability of discretisation schemes is fundamental to ensure that numerical roundoff errors do not grow with time and cause large errors in the numerical results. A standard way to analyse the stability of a discretised scheme is to use the von Neumann stability analysis, which assumes a Fourier series representation of the numerical error, and studies the behaviour of the Fourier coefficients as time increases. Unstable schemes cause a growth in the coefficients, and, conversely, stable schemes result in a decay of the coefficients. This paper analyses the stability of the resulting discretised scheme when subjected to numerical errors by way of the von Neumann stability analysis. This analysis gives insight as to the relationship between the parameter ranges, of both the physical and computational systems, required for numerical stability. © BHR Group 2008.
Rights: Copyright status unknown
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Appears in Collections:Aurora harvest 2
Civil and Environmental Engineering publications
Environment Institute publications

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