Study On Analytical Solution And Finite Point Method Of Soil Water Movement Equation

Water movement in unsaturated soils is the main compionent of natural water cycle,and plays an important role in irrigation and drainage of farmland and water resources evaluation.The study of analytical solution of water movement equation is of great significance for simulating soil water movement process and estimating soil hydraulic parameters.The time fractional soil water movement equation can be used to capture the non-Boltzmann transformation phenomenon of water transport in unsaturated porous media,which promotes the development of the analytical and numerical solutions of the equation.The main research work is as follows:(1)The research background and significance of soil water movement process arc introduced.The analytical solutions of soil water movement equation,time fractional soil water movement equation and meshless finite point method are summarized.At the same time,the basic theory of fractional calculus is given.(2)The vertical infiltration problem of one dimensional unsaiurated soil water is transformed into a functional extremum problem by using the least action principle and variational principle.By using Euler-Lagrange equation and integral mean value theorem,the functional extremum solution of soil water movement equation is obtained.Then,the modified functional extremum solution of vertical infiltration problem is given by using the analytical solution method of horizontal infiltration problem.The numerical results show that the modified analytical method proposed in this paper can accurately simulate the vertical infiltration process of unsaturated soil under the condition of uniform distribution of one dimensional initial water content,surface water accumulation or constant water head.(3)Based on the analytical solution method of classical horizontal infiltration problem,an approximate solution of one-dimensional time fractional horizontal infiltration problem is proposed.By comparing the error between the approximate solution and the numerical solution,the results show that the approximate analytical method is effective and suitable for predicting the abnormal diffusion process of water in unsaturated porous media.(4)For the one dimensional and two dimensional time fractional soil water movement equations,a finite point numerical algorithm based on L1 is constructed firstly.Secondly,it is proved that the discretization of the equation with respect to time is conditionally stable.Finally,the equation is numerically simulated and the results of numerical examples verify the effectiveness of the finite point method.