Accurate and efficient numerical solutions for the Saint Venant equations of open channel flow

Crossley, Amanda Jane (1999) Accurate and efficient numerical solutions for the Saint Venant equations of open channel flow. PhD thesis, University of Nottingham.

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Abstract

Within the eld of hydraulics there is a growing trend towards the use of computer based models, which have proven to be an invaluable tool in engineering. A range of commercial packages is available which encompass different mathematical models and a variety of solution strategies.

A number of problems can be identified with the software currently available, and as a result, research continues into developing better numerical techniques for computational hydraulics. The issues most often addressed by researchers consider the application of faster and more accurate numerical methods, many of which were originally developed for gas dynamics problems. There has been a growing trend in favour of Riemann based methods constructed within the finite volume framework. Such methods are noted for their good conservation and shock capturing capabilities. However, the computational cost of employing theses algorithms can lead to excessively long run times, particularly when higher order mathematical models are used. This often is as a result of stability constraints placed upon explicit schemes, which require the smallest possible time step permitted throughout the grid, to be applied globally. One possibility for improving this situation is to use local time stepping, whereby individual cells are advanced by their own maximum allowable time steps. To incorporate this concept into a transient model requires the development of a suitable integration strategy, to ensure that the solution remains accurate in time. Two such strategies developed for the Euler equations are considered within this thesis for application to the Saint Venant equations of open channel flow. Both techniques have been demonstrated to reduce run times and improve the quality of solutions in the regions of discontinuities. The investigation considers the the first order scheme of Roe, together with a second order extension constructed using a ux limiter approach. he eects of using an upwind based source term treatment, specifically developed for Roe's scheme, are also considered, and the source term calculations are incorporated into the LTS framework. Results are presented for a series of steady state and transient test cases, which illustrate how local time stepping can lead to reduced run times and improved solution accuracy. The results also highlight the benets of using an upwind source term treatment, particularly when variations in the channel geometry occur.

Item Type:Thesis (PhD)
Supervisors:Wright, N.G.
Uncontrolled Keywords:channel flow river modelling flood
Faculties/Schools:UK Campuses > Faculty of Engineering > School of Civil Engineering
ID Code:109
Deposited By:Nigel Wright
Deposited On:13 Jul 2005
Last Modified:06 Feb 2009 14:43

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