Abstract

CHAVEZ, Carlos; FUENTES, Carlos; ZAVALA, Manuel  and  ZATARAIN, Felipe. Finite difference solution of the Boussinesq equation with variable drainable porosity and fractal radiation boundary condition. Agrociencia [online]. 2011, vol.45, n.8, pp.911-927. ISSN 2521-9766.

The underground drainage is used to remove excess water in the root zone and in saline soils to leach salts. The dynamics of water is studied with the Boussinesq equation; its analytical solutions are obtained assuming that the aquifer transmissivity and drainable porosity are constants and that the free surface instantly lowers on the drains. The solution in the general case requires numerical solution. It has been shown that the boundary condition in the drains is a fractal radiation condition and the drainable porosity is a variable and is related to the moisture retention curve, and has been solved with the finite-element method, which in one-dimensional scheme can become equivalent to the finite-difference method. It is proposed here a finite difference solution of the differential equation considering the variable drainable porosity and fractal radiation condition. The proposed finite difference scheme has resulted in two formulations: in one the head and drainable porosity explicitly appear, variables linked to a functional relationship, which has been called mixed scheme; in the other only the hydraulic head appears, called head scheme. The two schemes coincide when the drainable porosity is independent of the head. The schemes have been validated with a linear analytical solution; for the nonlinearity has been shown that the numerical convergence is stable and concise. The numerical solutions is useful for the hydrodynamic characterization of the soil through an inverse modeling, and for a better design of the agricultural underground drainage systems as the assumptions used in the classical solutions have been eliminated.

Keywords : mixed formulation; head formulation; retention curve; inverse modeling.

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