处理土壤水垂直不饱和流问题的一种坐标变换方法

尽管土壤水不饱和流问题的数值求解已经广泛地被采用,但要了解土壤水不饱和运动的内在机理,解析解仍然是无法被取代的。由于土壤水不饱和流的非线性使得解析解的获得非常困难,特别是当考虑重力作用的不饱和流问题时,情况将变得更加复杂。所以直到目前,人们还没有得到考虑重力作用下的不饱和流方程的完整的解析解。本文提出了一种坐标变换方法,将重力作用下的不饱和流方程变成了与无重力作用的不饱和流方程完全相同的形式,进而首次获得了该问题的一个可用初等函数表达的解析解。本文所提出的坐标变换方法和所获得的解析解在实验上都得到了较好的验证。

AN APPROACH TO TRANSFORMATION OF COORDINATES OF VERTICAL UNSATURATED WATER FLOW IN SOIL

Even though the numerical solution of the unsaturated water flow in soil has been widely applied,the analytical solution cannot be replaced in understanding the intrinsic mechanism of water flow in soil. Considering the nonlinear in nature of unsaturated water flow in soil,analytical solutions should be extremely difficult to obtain,especially as the gravity is taken into consideration. Thus,so far,there is not any analytical solution available for those issues with both the gravitational effect and the nonlinearity under consideration. In this contribution,a coordinate transformation approach is suggested,enabling us to avoid the obstacle of the gravity by removing the item of gravitational effect in the equation. Subsequently,the equation for describing unsaturated water flow in the gravitational field bears the same form as the equation neglecting the gravitational effect. As a result,for the first time,an analytical solution that can be expressed with the algebra form is obtained. The relational theoretical results,including the new method of coordinate transformation and the analytical solution advanced in this paper,have been verified in experiments.