MIXED TRANSFORM FINITE-ELEMENT METHOD FOR SOLVING THE NONLINEAR 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, emp loys the mixed formulation of the Richards equation but expressed in t erms of a partitioned transform. An iterative finite element algorithm is derived using a Newton-Galerkin weak statement. Specific advantage s of the new method are demonstrated with applications to a set of one -dimensional test problems. Comparisons with the modified Picard metho d 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 wa ter zones. In addition, the mixed transform finite element method is s hown 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.