Numerical solution of the two-dimensional Richards ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Numerical solution of the two-dimensional Richards equation via a Taylor-Fréchet ELLAM technique
Author:Alvaro A. Aldama <> (Mexican Institute of Water Technology)
Victor Arroyo <> (Mexican Institute of Water Technology)
Presenter:Alvaro A. Aldama <> (Mexican Institute of Water Technology)
Date: 2006-06-18     Track: General Sessions     Session: General

The Eulerian-Lagrangian Localized Adjoint Method (ELLAM) has been succesfully employed in the solution of advection-dominated linear transport problems. Since the concept of adjoint operator only exists for linear equations, ELLAM is strictly speaking limited to linear problems. Some linearilization strategies have been proposed, such as the one based on a Picard type of scheme. Nevertheless, these strategies do not work well for the solution of highly nonlinear problems, such as those governed by Richards’ equation, that describes the flow of liquids in partially saturated soils. It is a well known fact that traditional Eulerian techniques, such as the Finite Difference or the Finite Element Method require the use of extremely fine meshes for the solution of Richards’ equation, particularly in cases where sharp moisture content or pressure gradients propagate through initially dry soils. This paper presents the development of a technique based on the Taylor-Fréchet expansion of the nonlinear two-dimensional Richards operator, following the characteristics of the governing equation, properly cast in an advection-diffusion-reaction format. Thus, the operator is linearized and a rapidly convergent solution technique is generated. Several examples that illustrate the application of the proposed procedure, incorporating a suite of different initial and boundary conditions are presented. A comparison with conventional Eulerian methods and the Picard linearlization procedure clearly show the superiority of the Taylor-Fréchet ELLAM technique. Keywords : Unsaturated soils, Richards’ equation, ELLAM, Taylor-Fréchet expansion.