同伦分析法推求Green-Ampt方程显格式精确解

An explicit exact solution of Green-Ampt equation by Homotopy Analysis Method

针对Green-Ampt(GA)积水入渗模型只有隐格式解的问题,利用同伦分析法(HAM)给出GA方程的显式解析解。首先构造一组基底为幂函数的显示解表达,通过选择合适的线性和非线性算子,定义零阶形变方程。为保证HAM的系数遍历原则,给出了零阶形变方程中辅助函数的选择形式,还探讨了辅助参数对不同级数解收敛性的影响。通过与其他近似解的比较,验证了所提方法具有理论严谨完备、计算稳定性好、结果精度高的特点,能有效模拟降雨条件下积水入渗的过程。

Aiming at the problem that Green - Ampt infiltration model only has implicit solution, we use Homotopy Analysis Method to obtain an explicit form of exact solution. A group of explicit solution expressions am constructed in terms of power function basis and then by choosing appropriate linear and nonlinear operators, a zero - order deformation equation can be defined. In order to ensure the rule of parameter ergodicity in HAM , the form of the auxiliar function in zero - order deformation e-quation is determined. Meanwhile , the influence of auxiliar parameter is discussed regasolutions. Through the comparisons with other approximate solutions , it can be verified that the presented method has the characteristics of rigorous theor basis , stable numerical performance and good accuracy. It can be appliedtion process under rainfall condition.