Analysis And Simulation Of Upwind Mumerical Methods For The Unsaturated Water Flow Problem

The flow of groundwater in the homogenous soil,when soil interstice is not completely full of water,can be contributed to the unsaturated soil water flow.It is an important form of water flow in porous medium.In this paper, a one-dimension unsaturated flow problem with different time-space distribution of concentration of water is considered.Assume that z axis vertically downwards.and take the earth's surface as origin. Let Q{z, t) is concentration of water in soil at z and t,where z is the distance away from the surface and t is time variable. Assume the permeability or evaporability on the ground depends on t. Permeability is positive while evaporability is minus.The distribution of concentration of water at the bottom also depends on t.By the virtue of the Darcy law and continuity theory,the unsaturated soil water flow problem can be described as the following model[3-6]:Seek Q subject towhere Q is related to volume concentration of water.Sr the bibulous rate of roots. K(Q) the hydro-power transport coefficient,D(Q) the soil water diffusivity.q(t),β(t) and Q₀(z) are respectively the water flux at the upper boundary.lower boundary and the concentration of water at the initial time.When z is large.the change of Q(z, t) is small with the different temperature at the surface.so we can assume dβ/et≈ 0. K...