A physically based , two - dimensional , finite - difference algorithm for modeling variably saturated flow

A computationally simple, numerical algorithm capable of solving a wide variety of twodimensional, variably saturated flow problems is developed. Recent advances in modeling variably saturated flow are incorporated into the algorithm. A physically based form of the general, variably saturated flow equation is solved using finite differences (centered in space, fully implicit in time) employing the modified Picard iteration scheme to determine the temporal derivative of the water content. The algorithm avoids mass-balance errors in unsaturated regions and is numerically stable. The resulting system of linear equations is solved by a preconditioned conjugate gradient method, which is known to be computationally efficient for the type of equation set obtained. The algorithm is presented in sufficient detail to allow others to implement it easily, and is verified using four published, illustrative sets of experimental data.