Mixed Transform Finite Element Method for Solving the Non-Linear Equation for Flow in Variably Saturated Porous Media

A new computational method is developed for numerical solution of the Richards equation for flow in variably saturated porous media. The new method, referred to as the mixed transform finite element method, employs the mixed formulation of the Richards equation but expressed in terms of a partitioned transform. An iterative finite element algorithm is derived using a Newton–Galerkin weak statement. Specific advantages of the new method are demonstrated with applications to a set of one— dimensional test problems. Comparisons with the modified Picard method show that the new method produces more robust solutions for a broad range of soil– moisture regimes, including flow in desiccated soils, in heterogeneous media and in layered soils with formation of perched water zones. In addition, the mixed transform finite element method is shown to converge faster than the modified Picard method in a number of cases and to accurately represent pressure head and moisture content profiles with very steep fronts.