黄土沟壑区坡面入渗-产流方程推导及数值解法

Formula deduction and numerical solution of infiltration and runoff equation on Loessial Hillslope

从修正的Green-Ampt方程出发,通过数学推导将常微分形式的Green-Ampt入渗方程转化为超越方程求解,从而简化了Creen-Ampt方程的计算过程;对坡面流运动波方程,给出了推导过程和四点隐式差分求解方法.简化为超越形式的入渗方程经牛顿迭代和四阶龙格-库塔算法求解,可以保证解的收敛和稳定,牛顿迭代相比龙格-库塔方法计算精度更高;在坡面土槽进行恒降雨强度的3场降雨冲刷试验,利用三维激光扫描仪获取生成的DEM数据,检验在l mm网格精度下的入渗和产流模拟结果,结果表明坡面流过程的模拟计算结果与实测资料符合良好,可用于模拟坡面入渗和产流过程,入渗误差可控制在12%以内,流量误差在13.1%以内,模拟的入渗率和流量均比实测值偏大,且模拟入渗率误差与流量误差呈正相关.

From the modified Green- Ampt infiltration equation,the differential form of the equation was changed into transcendental equation solution by the mathematical derivation,therefore,the calculation process was simplified.Considering the slope movement wave equation,the derivation process and four implicit difference solution methods were provided.The simplified transcendental infiltration equation was calculated by Newton iteration and fourth order runge- kutta algorithm,and the convergence and stability of the equation was guaranteed,when the accuracy of the Newton iterative calculation is higher than the runge- kutta method.Three rainfall scouring experiments with the constant rainfall intensity were carried out to vahdate the simulation on infiltration,and the flow with a grid precision of 1 mm was generated by the DEM data obtained from the Lidar.The results show that the simulation results of slope surface flow process are in good agreement with the measured data,and infiltration errors can be controlled within 12%,while the flow rate error can be widiin 13.1%.The simulated infiltration rate and the flow rate are larger dian diat in the measured results,and the simulated infiltration rate error and flow rate error are positively correlated.