We present two new segments to the growing analytic element method. First, we present an iterative solution for the unsaturated analytic element method using a full constitutive hydraulic properties system. The so called “Gardner soil” is limited in that its hydraulic conductivity function does not fully comply with all soil types. Several matching methods were suggested in the past to compare the Gardner soil with more flexible functions such as the van Genuchten – Mualem, and the Brooks and Corey. We present here a piecewise matching methodology of Gardner parameter to the van Genuchten –Mualem function with specific application to the unsaturated analytic element method.

Second, we present an application of the analytic element method for diffusion – sorption processes at the aggregate scale. The analytic element method was traditionally used to model water flow in steady saturated porous media. Recent applications expanded the use of the method to transient flow, and to unsaturated flow. Here we expand the use of the method to model diffusion processes within a soil aggregate subjected to chemical sorption. This expansion of the method provides a tool for modeling the interrelated effect of individual grains within an aggregate, resulting in effective sorption coefficients.