Finite Analytic Numerical Solutions for Unsaturated Flow with Irregular Boundaries

Abstract

This study illustrates the development of the finite‐analytic (FA) numerical solutions associated with an optimal (variable) time‐weighting factor for water flow in unsaturated porous media with irregular boundaries. This method entails the nine‐point and five‐point elements such that it can simulate quite well the irregular flow domain without using boundary‐fitted transformation. For an element near the irregular boundaries, a five‐point FA algebraic solution is derived; for a regular element, the nine‐point FA algebraic equation is used. In execution of numerical computation, the irregular five‐point boundary element is recasted into the nine‐point element, allowing a regular structured grid system to be used to solve for the water flow in an irregular domain. Two problems are solved in this study. The first is a transient, two‐dimensional flow of water under a strip source infiltration of constant flux with regular boundaries. Uniform clay loam, uniform coarse sand, and layered system of soil are used in the numerical simulation. It is shown that the finite‐analytic numerical solutions conform to accuracy and numerical stability very well. Mass conservation for the FA method also is illustrated. The second problem simulates unsaturated flow of leachate from landfill with irregular boundaries. The water pressure head and content in the unsaturated zone are predicted as a function of time and space.