Orthogonal collocation and alternating-direction procedures for unsaturated flow problems

The alternating-direction collocation method has recently been developed for general parabolic equations. In order to test the applicability of the procedure to highly nonlinear problems, an alternating-direction collocation algorithm is developed to simulate two-dimensional flow in unsaturated porous media. The algorithm employs an alternating-direction solution procedure within the framework of a modified Picard iteration scheme. Numerical behaviour of the new procedure is compared to the behaviour of a standard two-dimensional collocation formulation. The new method is also tested on several infiltration problems of practical interest, including a layered and sloping soil. Results demonstrate the method to be accurate and highly mass conservative. The algorithm also produces significant savings in both execution time and storage.