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An approximate solution of fokker-planck equation for one dimensional groundwater recharge through porous media

The nonlinear Fokker-Planck equation arising for onedimensional groundwater recharge through porous media, is in the form of partial differential equation which has been solved by using Homotopy Analysis method with the help of first approximate solution ( ) 0 , Z T θ for given auxiliary parameter 0 q = . The solution is physically interpreted and concluded that during onedimensional recharge through unsaturated porous media, the moisture content of the soil is parabolically increasing as depth Z increases for given 0 T > . The graph of the solution is given by using Maple coding. INTRODUCTION The uses of analytical techniques for groundwater flow and mass transport in the unsaturated porous media has significant increasingly from last few years, and it has a great important for hydrologist, agriculturists and people related with water resources sciences. Analytical solution provides better insight into the physics behind the transport phenomenon and efficient to use. Analytical approaches are for the most limited to situations of simple geometry domains, linear governing equation and homogeneous porous media. Analytical solutions of the partial differential equation for unsaturated flow under various boundary and initial condition are difficult to obtain because of the nonlinearity in soil hydraulic parameters. Exact analytical solution typically requires specialized forms of the hydraulic conductivity and diffusivity functions for nonlinear diffusion-advection equation. Several investigators have described different relation between the diffusivity coefficient and volumetric water content problems in unsaturated porous media. In 1958 Gradner [6] model provides a relationship between the pressure head 'h' and the volumetric water content θ as, ( ) b h a θ θ − = ⋅ where a & b are empirical constants. The exponential hydraulic conductivity function has been widely used, but it is known to have a limited range of application to many real soils. The Brooks-Corey model [4] is a relationship between the reduced water content * θ and the soil suction. The reduced water content * θ is defined as a function of two values of moisture: the saturation of the moisture s θ and the residual of the moisture r θ ; * r