10.4122/1.1000000703
Aldama, Alvaro A.
Alvaro A.
Aldama
aaldama@tlaloc.imta.mx
Arroyo, Victor
Victor
Arroyo
vmarroyo@tlaloc.imta.mx
Aldama, Alvaro A.
Alvaro A.
Aldama
aaldama@tlaloc.imta.mx
Numerical solution of the two-dimensional Richards equation via a Taylor-Fréchet ELLAM technique
XVI International Conference on Computational Methods in Water Resources
2006
2006
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.