The Numerical Solution Of The Soil Water Power System Analysis And Applied Research

Based on the energy state of soil moisture content, soil hydrodynamics studies water flow, solute and heat transport in unsaturation soil. In this paper, water flow and solute density in soil hydrodynamics have been studied. Since the problems are described by some nonlinear equations, it is impossible to obtain their analytical solutions except for special cases. Therefore, numerical approximations are used to solve the equations by means of generalized difference method, mixed finite element method and proper orthogonal decomposition method. The existence of generalized solutions of their variational problems, numerical solutions as well as the error estimates are discussed, the numerical examples are proposed. So both the theory researches and the actual computational examples are given in this paper. In the theory respect, the suitable mathematical bases of numerical solutions for soil hydrodynamics are proposed; in the respect of actual computational methods and numerical examples, the procedure of the reasonable numerical solutions for these equations are provided. The methods may be used too by engineers for reference and be applied to the actual computations of more complicated soil hydrodynamics.This paper is divided into six chapters. Chapter one is introduction. Prom chapter two to chapter four, generalized difference method, mixed finite element method and mixed finite element-upwind generalized difference method are used to approximate 1-D unsaturated soil water flow problem, solute density problem and the coupled transport problems of unsaturated soil water flow and solute. A numerical model for the 2-D unsaturated soil water flow equation is established with finite volume element method in chapter five. In chapter six, proper orthogonal decomposition method is introduced to solve the 2-D solute transport problems.The work in this paper is our main researches for three years. It is a new attempt that is first presented by us treating 1-D unsaturated soil water flow problem, solute density problem and the coupled transport problems of unsaturated soil water flow and solute. To the our knowledge, the total attempting report which is similar to or parallel to chapter five and chapter six hasn't been seen. Therefor, that maybe to say that the results in this paper is of peculiarity.