入渗Richards方程Laplace变换步骤中原函数敛散性的讨论  

Discussion on convergence of primitive functions in Laplace transform on Richards equation

作　　者：朱悦璐 王义成[2] ZHU Yuelu;WANG Yicheng(College of Water Conservancy and Ecological Engineering,Nanchang Institute of Technology,Nanchang330099,China;China Institute of Water Resources and Hydropower Research,Beijing100038,China)

机构地区：[1]南昌工程学院水利与生态工程学院,江西南昌330099 [2]中国水利水电科学研究院,北京100038

出　　处：《中国水利水电科学研究院学报（中英文）》2023年第5期476-481,489,共7页Journal of China Institute of Water Resources and Hydropower Research

基　　金：国家自然科学基金项目(52069014);江西省科技厅应用培育计划(20181BBG78078)。

摘　　要：传统求解非线性Richards方程的Laplace线性化方案中,未考虑原函数θ(z,t)的敛散性,均默认原函数收敛或发散程度较小,这在一般情况下是可行的,但在极端理论条件下,例如原函数不收敛或发散速度较快时,往往会引起较大计算误差。针对这种情况,本文建议在变换前,先通过初步试验,确定入渗曲线形态,进而判断原函数敛散性,通过增加该步骤以确保计算的数学物理意义。文中通过算例,证明了多项式曲线、幂函数曲线满足Laplace变换条件,幂指数函数不满足变换条件,并通过一个实际反例验证了这一结论。本文所讨论内容,可作为非饱和土力学理论的一个补充。When the nonlinear Richards equation is solved by Laplace transform,the nature of the original function is usually not considered,and the degree of convergence or divergence of the original function is assumed to be small.Thus,the results are usually satisfactory.However,under extreme conditions,for example,the original function does not converge or the divergence speed is fast,large calculation errors are often caused.In view of this situation,it is suggested that the morphology of the infiltration curve and the convergence of the original function should be determined by a priori test,so as to judge the rationality of solution by Laplace transform.The analytical results show that the condition of Laplace transform is satisfied when the original function is polynomial and power function.However,when the original function is a power exponential function,the applying condition is not satisfied,which is verified by a case.This study improves the solution process of Richards equation and compensates for possible errors.

关 键 词：非饱和入渗 RICHARDS方程 LAPLACE变换 非线性微分方程 函数敛散性 

分 类 号：TV138[水利工程—水力学及河流动力学] TU43[建筑科学—岩土工程]