A MATLAB method of lines template for transport equations
Author(s)
Lee, HS
Matthews, CJ
Braddock, RD
Sander, GC
Gandola, F
Griffith University Author(s)
Year published
2004
Metadata
Show full item recordAbstract
Many environmental problems involve diffusion and convection processes, which can be described by partial differential equations (PDEs). This paper will describe the development of a MATLAB template that generates a numerical solution to PDEs using the method of lines. The template will be applied to various unsaturated flow problems within soil physics to demonstrate the versatility of the method. In particular, the template will generate solutions for three cases (1) one-dimensional Richards' equation for vertical infiltration; (2) coupled one-dimensional Richards' equation and solute transport equation for horizontal water ...
View more >Many environmental problems involve diffusion and convection processes, which can be described by partial differential equations (PDEs). This paper will describe the development of a MATLAB template that generates a numerical solution to PDEs using the method of lines. The template will be applied to various unsaturated flow problems within soil physics to demonstrate the versatility of the method. In particular, the template will generate solutions for three cases (1) one-dimensional Richards' equation for vertical infiltration; (2) coupled one-dimensional Richards' equation and solute transport equation for horizontal water and contaminant flow; and (3) two-dimensional Richard's equation for unsaturated flow over a complex geometry. Where possible, the results from the template will be compared against analytical solutions to determine the accuracy of the numerical solution. In addition, the paper will provide a discussion on possible extensions to the template and future directions.
View less >
View more >Many environmental problems involve diffusion and convection processes, which can be described by partial differential equations (PDEs). This paper will describe the development of a MATLAB template that generates a numerical solution to PDEs using the method of lines. The template will be applied to various unsaturated flow problems within soil physics to demonstrate the versatility of the method. In particular, the template will generate solutions for three cases (1) one-dimensional Richards' equation for vertical infiltration; (2) coupled one-dimensional Richards' equation and solute transport equation for horizontal water and contaminant flow; and (3) two-dimensional Richard's equation for unsaturated flow over a complex geometry. Where possible, the results from the template will be compared against analytical solutions to determine the accuracy of the numerical solution. In addition, the paper will provide a discussion on possible extensions to the template and future directions.
View less >
Journal Title
Environmental Modelling and Software
Volume
19
Publisher URI
Copyright Statement
© 2004 Elsevier : Reproduced in accordance with the copyright policy of the publisher : This journal is available online - use hypertext links.