传统入渗Parlange解中存疑步骤的讨论与改进

Discussion and improvement of questionable steps in traditional infiltration Parlange solution

为解决Richards入渗方程Parlange解中关键参变量c(t)难以计算的问题,本文设计一种基于试验假设分离变量的参数方程方案,将含有c(t)的积分方程转化为超越方程并求解析解。新方案计算结果表明,当试验参数D(θ)、K(θ)为幂函数时,改进模型收敛较快,通过十余次迭代即可获得稳定解,所生成的土体含水率运动轨迹曲线符合实际。方案对比结果表明,新方案与传统Parlange化简方案对比结果存在较大差异,与Philip级数解对比结果已十分接近,二者误差不超过5%;改进后的计算方案具有严格解析步骤和明确数学意义,可作为Parlange模型在关键计算步骤上的一个补充。

In order to solve the problem that the key parameter c(t)in the Parlange Solution of Richards Equation is difficult to calculate,this paper proposes a variable separation method based on experimental hypothesis,which transforms the integral equation containing c(t)into transcendental equation and finds the analytical solution.The calculation results show that when the test parameters D(θ)and K(θ)are power functions,the improved method converges quickly,and a stable solution can be obtained by more than ten iterations,the generated trajectory curve of soil water content is in line with the reality.The comparison results show that there is a big difference between the new scheme and the traditional Parlange simplification scheme,which is very close to the Philip series solution,and the error between them is less than 5%;The improved calculation method has strict analytical steps and clear mathematical significance,which can be regarded as a supplement to the Parlange model in a key step.