同伦分析法推求Green-Ampt方程显格式精确解

发布时间：2018-01-07 22:25

本文关键词：同伦分析法推求Green-Ampt方程显格式精确解　出处：《人民长江》2017年16期 　论文类型：期刊论文

【摘要】：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。
[Abstract]:To solve the problem of Green-AmptGA-based water infiltration model with only implicit scheme solution. The explicit analytic solution of GA equation is given by means of homotopy analysis method. Firstly, a set of explicit solutions with the base of power function is constructed, and the appropriate linear and nonlinear operators are selected. The zero order deformation equation is defined. In order to guarantee the coefficient ergodic principle of HAM, the selection form of auxiliary function in zero order deformation equation is given. The influence of auxiliary parameters on the convergence of different series solutions is also discussed. By comparing with other approximate solutions, it is verified that the proposed method has the characteristics of rigorous theory, good calculation stability and high precision. It can effectively simulate the process of water infiltration under rainfall.
【作者单位】：长江工程职业技术学院;武汉大学土木建筑工程学院;
【分类号】：O302
【正文快照】： 1研究背景Green-Ampt(GA)入渗方程是由Green和Ampt在1911年提出的基于毛管理论的积水入渗模型,与描述非饱和土壤水分运动复杂形式的Richards方程相比,该方程形式简单,具有明确的物理意义。GA方程所需土壤的物理参数也比较容易获得,这使得其在非饱和土的入渗过程研究中有着广泛

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