Cell Analytical-Numerical (CAN) method for the solution of the Richards equation.

摘要

In this paper, we develop and describe implementation of the Cell Analytical-Numerical (CAN) method for solution of the one-dimensional Richards equation. The CAN method incorporates the local analytical solution and the continuity of the soil moisture flux across computational clement boundaries to construct an algebraic relationship between the values of the dependent variable on the boundaries of adjacent elements. The time derivative is approximated by a fully implicit scheme. Assembling all the elements together produces a tridiagonal matrix equation which is efficiently solved via the Thomas algorithm. This system of nonlinear algebraic equations is solved iteratively via an implicit linearization scheme. Accuracy is assessed by comparison to semi-analytical and Finite Element solutions. The results indicate CAN's high accuracy over a wide range of soil types.