非饱和土壤水—维水平运动方程的拟解析解及其验证*

本文讨论了土壤水—维不饱和水平流方程的解析解问题.文中首先根据土壤水扩散率D与土壤含水量θ之间的经验关系.对原土壤水—维不饱和流方程作变量代换,将方程变为易于求解的形式,然后采用变量分离的方法并结合Boltzmann变换法进行求解.从而得出了解析表达式.同时这个解析解在土壤水—维水平不饱和流实验中得到了验证,从而证明了其解析表达式的正确性。

Almost Analytic Solutions and Their Tests of the Horizontal Diffusion Equation for the Movement of Water in Unsaturated Soil

This paper discusses the analytic solutions of the diffusion equation.for the movement of water in unsaturated soil. Firstly, according to the experience relation between the diffusivity "D(θ)" and water content in soil "θ",and through variable substitution, the original diffsion equation is converted into the form easy to solve.Then, the variables separution method together with the Boltzmann transform methodis used to find out the solution of the new partial differential equation. So the analytic function of θ(x,t) is obtained, which is verified by the experiment of water flow through unsaturated soil.