An analysis of the Talbot-Ogden model and its extension in the moisture content domain.

摘要

Two classical equations based on Darcy's law for unsaturated flow are the Richards equation and the Green-Ampt equation. Based on the Green-Ampt equation, the recent unconditionally mass-balanced Talbot-Ogden model discretizes the moisture content domain into vertical bins so that the Green-Ampt equation is applied piece-wisely for each bin. The present dissertation makes a detailed analysis of the relationship between the increment in the number of bins and the infiltration rate in the Talbot-Ogden model. Using rigorous proof, it reveals that more bins can generate a larger infiltration rate. An asymptotic analysis produces insights into the influence of this discretization on the infiltration with an infinite number of bins. The analysis also gives an upper bound to the infiltration rate, which is illustrated by numerical experiments on coarse and fine soil textures. The Talbot-Ogden model is extended to a new model with a two-dimensional moisture content domain by keeping the spatial domain. This extended model inherits the infiltration phase in the Talbot-Ogden model. However, the difference in this extended model is directional redistribution, which is based on the gradient of the porosity functional. Algorithms are proposed for the extended model, and numerical experiments are conducted. The flexibilities of the extended model for different soil textures are proven by analysis based on the probability distribution function of porosities. Another three-dimensional moisture content domain is constructed for further extension of the Talbot-Ogden model.