Density-dependent flow in one-dimensional variably-saturated media

Abstract

A one-dimensional finite element model is developed to simulate density-dependent flow of saltwater in variably saturated media. The flow and solute equations were solved in a coupled mode (iterative), in a partially coupled mode (non-iterative), and in a completely decoupled mode. Pressure head was considered as the dependent variable in the fluid motion equation, and a backward Euler scheme with mass lumping was used for time discretization of both flow and transport equations. The modified Picard method was used in the flow equation to solve for pressure heads. The model was verified by comparison to an analytical test function and published numerical results. It was found that density effects on the flow decreased with the pressure head. However, significant effects can still be observed at relatively low (negative) pressure heads. The density dependence effects were at their maxima at steady state. Partial coupling of the flow and transport equations was shown to give satisfactory results in comparison with full coupling. The advantage in partial coupling is a reduced amount of numerical computation. The finite element formulation of the model is presented in a form that allows a person with finite difference expertise to implement it easily.