二维非饱和土壤水分运动方程的径向基配点差分法

Radial Basis Function Collocation Difference Method for Two-dimensional Water Movement Equation in Unsaturated Soil

针对二维非饱和土壤水分运动方程,将径向基配点法结合差分法构造了一种新的数值算法.该算法先采用差分法处理非线性项,再利用径向基函数配点法的隐格式求解方程,避免了因非线性项的存在导致不能直接使用配点法的现象,并且证明了该算法解的存在唯一性。通过对非饱和土壤水分运动的数值模拟,并采用试验数据对新算法进行了验证,模拟结果与试验结果非常吻合,表明该算法实用、有效。同时,比较分析了不同径向基函数以及不同算法的模拟精度,结果表明,与MQ函数和Guass函数相比,新的径向基函数具有更好的模拟精度,且相对于有限差分法和有限元法,本文提出的方法具有一定的优越性.

A radial basis function collocation method combined with difference is devel-oped, which based on the collocation method and radial basis function interpolation for Two-dimensional water movement equation in unsaturated soil. This method first uses dif-ference method to deal with the nonlinear term, and then solves the equation by using implicit scheme of the equation. Moreover, the existence and uniqueness of the solution to the method is established. According to the numerical computing example results, it indicates that the new radial basis function has the best simulated precision than MQ func-tion and Gauss function. Furthermore, as compared with other methods, this algorithm is practical and effective.