Finite Element Method For The Coupled Problem Of Controlled-release In Unsaturated Soil Water Flow

With the development of agriculture technology, fertilizers and pesticides are extensively used to improve production efficiency in the agricultural production. According to the previous statistics of Environmental Protection Department, China is the most used fertilizers and pesticides in the world. The amount of usage of fer-tilizers and pesticides is in 4,700 million tons and 130 millon tons, respectively, but the effective rate is only 30 percent. Excessively using fertilizers and pesticides makes the farmland quality descend, and a great loss of them causes environment pollution. More and more fertilizers and pesticides are used to increase output in the meantime, which results in a vicious circle. It causes bio-diversity to decline, ecological stability to decrease, and food structure to reduce gradually. In order to reduce this deterioration, the green food has been born at the right moment. Although it can reduce the environment impact, there are notability defects such as high cost and low yield in modern technology. It is impossible to use the technology in large-scale for meeting a lot of demand in modern agricultural production, there-fore, how to improve the utilization ratio of fertilizers and pesticides has been an important research topic in the present. In order to reduce the damage to use fertil-izers and pesticide to the utmost, the new technology, known as controlled-release, has been invented in the modern agriculture. What is called the controlled-release is that the solute, installed in the capsule material with permeability, is released into the soil through the capsule and spread in the soil. It both raises the utilization ratio and reduce the environment disruption. The soil is in the unsaturated state in the process of controlled-release. Zhenghui Xie, Zhendong Luo, Huanrong Li gave the error analysis and numerical simulation for the water content and flux in the unsaturated soil water flow, respectively. Zhen-dong Luo gave the numerical solution with mixed element method, and Huanrong Li did it with generalized difference method. Friedman gave general controlled-release process and one dimension numerical solution. Given the stable velocity field, Aijie Cheng discussed the finite element method for the coupled problem of controlled-release-transport in three dimensions. Chunmei Zuo gave the three dimensions finite element analysis for the coupled problem of controlled-release-transport in the saturation.In this dissertation, the coupled problem of controlled-release in the unsatu-rated soil water flow is studied. The dissertation is divided into four chapters:In the first chapter, we give the relationship of the water content and flux, the rela-tionship of the solute in the transport process, and the assumption for the boundary conditions. In the second chapter, we solve the water content and flux of the unsat-urated soil water flow by Raviart-Thomas mixed finite element and the optimal error estimate for semi-discrete and time-discrete scheme is given, respectively. In the third chapter, we solve the solute concentration of the unsaturated soil water flow by a standard Galerkin method and the suboptimal error estimate is given. The linear extrapolation for the water content and flux in the solute concentration equa-tion is introduced in the event that the variation of the water content and flux with the time is much smaller relative to the solute concentration at the same condition. In the fourth chapter, on the basis of periodic boundary condition, given that the diffusion coefficient is very small and the convection is dominating the process in the equation, we establish the modified method of characteristics -MMOC scheme and make theoretical analysis. Considering the MMOC scheme is not conservable, we introduce the perturbationδ=γhc(?)Δtc and give the modified method of char-acteristics with adjusted advection-MMOCAA scheme. At last, one-dimensional simple numerical example that water content and flux is in the first boundary con-ditions and the solute concentration is in the second boundary conditions is given. We solve the water content and flux of the unsaturated soil water flow by one times Raviart—Thomas mixed finite element method and substitute the results into the solute concentration equation. The result reveals MMOC scheme is much better than Galerkin scheme in the stabilization and computing speed aspect.