Saturated-unsaturated mass transport modeling by finite element method

A two-dimensional finite element model is proposed to simulate the movement and distribution of contaminant in groundwater flow systems. The complete soil system is treated as a continuum encompassing flow in both saturated and unsaturated zones. In the unsaturated zone, the air phase is assumed continuous and under atmospheric pressure, therefore, only the flow or water is considered. The water discharge velocity is assumed to be defined by Darcy's law in both the saturated and unsaturated zones. The model involves the solution of two governing equations, a transient seepage equation and an advection - dispersion equation. The finite element solution to the two governing equations is based on the Galerkin weighted - residual method. For transient analysis, both the time centered difference and backward difference schemes are employed to march forward in the time domain. The nonlinearity of the seepage equation is solved by iterative techniques. The computed velocities from the seepage equation are subsequently used in computing the concentration distribution of contaminant with time. The model can accommodate both steady state and transient flow conditions. Due to the extreme flexibility of the finite element technique, the model can handle complex geometries with arbitrary degrees of heterogenity and anisotropy. Changing boundary conditions during the transient process can also be handled as specified step functions. Example problems are presented to demonstrate the capability of the model