Techniques for improving numerical modeling of water flow in variably saturated, heterogenous media.

摘要

We introduce a simple nonlinear transformation. The new approach was compared to Kirkland's φ-based method and Ross' p-based method as well as Celia's h-based method. All algorithms use the modified Picard iteration with a linear solver of the Cholesky preconditioned conjugate gradient method (2-D) and with Thomas' method (1-D). An adaptively optimum relaxation procedure was also proposed to improve the efficiency and the robustness for 2-D cases. To test the effects of the transformation and the optimal relaxation. a total of 14 different 1-D and 2-D infiltration cases were considered. The results show that the newly introduced P(t)-based method is the most effective of the four methods and the simplest of the three transformation methods. It is several orders of magnitude faster than the h-based method and also reduces the truncation error using the same grid. The proposed adaptively optimum relaxation procedure, enhances the efficiency and robustness of all four methods to different degrees. Combination of the P(t)-based method with the adaptively optimum relaxation procedure results in a very efficient and robust algorithm. Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front when a traditional mass-distributed finite element method is used.