Comparing two new transformations for the water content form of Richards' Equation

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Title Comparing two new transformations for the water content form of Richards' Equation
Author Matthews, Christopher John; Cook, Freeman J.; Braddock, Roger David; Knight, John Howard
Publication Title Proceedings of the 14th IASTED International Conference: Applied Simulation and Modelling
Editor M.H. Hamza
Year Published 2005
Place of publication USA
Publisher ACTA Press
Abstract This study will present two new transformations that are applied to the water content (θ) form of Richard's Equation: 1) a reference soil transformation and 2) a constant “relative gradient ratio” transformation. The reference soil transformation enables a model to simulate water flow in a given soil in terms of θ for a reference soil. The main advantage of this transformation is that it provides a continuous θ profile across soil layers. However, the choice of a reference soil could also provide some numerical advantages by, for example, minimising the effect of sharp wetting fronts. An analytical expression will be derived that approximates the effect a transformation has on the gradients within a system. This approximation is based on the notion of relative gradients and will assist in analysing, which reference soils are appropriate for the problem. In addition, the analytical approximation can be used to derive general transformations for partial differential equations (PDEs). For this study, we will derive a constant “relative gradient ratio” transformation that will decrease relative gradients within the system by a constant factor (ε). Using the Method of lines (MOL), numerical solutions will be generated for a test case from the literature for both transformed and non-transformed equations. By comparing these solutions, this paper will analyse whether the new transformations improve the efficiency and/or accuracy of the numerical solution for the test case problem.
Peer Reviewed Yes
Published Yes
Publisher URI http://www.actapress.com/Content_of_Proceeding.aspx?proceedingID=304
Alternative URI http://www.actapress.com/Abstract.aspx?paperId=20863
Copyright Statement Copyright 2005 IASTED and ACTA Press. Use hypertext link for access to the publisher's website.
ISBN 0889864691
Conference name 14th IASTED International Conference: Applied Simulation and Modelling
Location Benalmádena, Spain
Date From 2005-06-15
Date To 2005-06-17
URI http://hdl.handle.net/10072/2738
Date Accessioned 2005-12-19
Date Available 2009-08-13T06:44:43Z
Language en_AU
Faculty Faculty of Environmental Sciences
Subject PRE2009-Environmental Engineering Modelling
Publication Type Conference Publications (Full Written Paper - Refereed)
Publication Type Code e1

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