Characteristics Methods For The Unsaturated Soil Water Flow Including Pollution Problem

The research of the model of groundwater pollution is meaningful on reasonable economic development and management of groundwater resources and understand-ing the transport law of matter and energy in porous media. In the problems of environmental pollution, the mathematical model of groundwater pollution also has important theoretical and value in use.According to Darcy theorem, we can get the model of problems of unsaturated soil water flow which include pollution:To solve c which can satisfy the following for any t>0:δΩis piecewise smooth,0 is the soil moisture.c is the concentration of pollutants,k(0) is the hydraulic conductivity,D(0) is the diffusion rate,t is the time, z is the posi-tion coordinates.Origin is in the surface,and downward direction is positive,x,y is the horizontal coordinates.I is the pollution source and sink terms,and in this pa-per we consider it as zero.q is the water flux, which is per unit time per unit area of water.Sr is the soil factor,and in this paper we also consider it as zero.d is the diffusion coefficient.Characteristic finite difference method proposed by Douglas,Russell,can sub- stantial increase in time step and in accuracy.Using this method,we sign f=q/θ,and on the condition of one-dimensional.we signΨ=(?).τ(z,t) is corresponding characteristic direction of the unit vector of operator of Then.we can get the error estimates:For the Characteristic finite difference method,we also give the error analysis of two-dimensional problem.SignΨ=(?).τ(z,t) is corresponding character-istic direction of the unit vector of operator of And the error estimates is:...