Characteristics Finite Difference Methods And Numerical Simulation For The Unsaturated Soil Water Flow Problem

The flow of ground water in the homogeneous soil when soil water is not completely full of interstice can be contributed to the unsaturated soil fluid flow. It is an important form of water flow in porous medium. The forecast of unsaturated water flow has the important significance in atmosphere science, pedology, agricultural engineering, environment engineering and ground water dynamics, etc. The process of surface and ground water flow, such as atmospheric precipitation, evaporation and transpiration, surface's water leakage, absorption of roots and ground water flow, etc, all can be taken as unsaturated water flow . It is very difficult to get analytic solution except some very specific cases for the model owing to nonlinear partial differential equation. Therefore, it is the typical way that uses numerical approximation to solve unsaturated equation. Zhenghui Xie avoided concussive non-physical solution using the method of lumped masses, while it only gave the simulation of soil water contents. Zhendong Luo established a conservation form of unsaturated soil flow.It can solve the distribution of ground water and its flux, and improve flux accuracy using traditional discrete methods.Basing on horizontal resolving power of the atmospheric circumfluent mode(1-5 longitude and latitude), soil water flow in horizontal direction can be ignored. We consider one dimension unsaturated water flow problem, water-bearing rate has different space-time distribution. Assume z axis vertically downwards, and take ground as grid origin. Q(z, t) is the water-bearing rate at t time in z under ground. Assume ground has various infiltration or evaporation rate with time, infiltration rate is plus, evaporation rate is minus. And in the bottom water-bearing rate varieties with time. Accordingly.in virtue of Darcy law and continuity theory, unsaturated soil water flow problem can be given by the following model equations:For arbitrary T > 0, let Q satisfy:f " ï¿¡(W)f?) + ^ = Sr,0(z,Q) dz K 'Then,(l)can be written in the equivalent form = sr,o