NUMERICAL SOLUTION OF BOUSSINESQ EQUATION ARISING IN ONE-DIMENSIONAL INFILTRATION PHENOMENON BY USING FINITE DIFFERENCE METHOD

Abstract

Infiltration is a gradual flow or movement of groun dwater into and through the pores of an unsaturated porous medium (soil). The fluid infiltered in porous medium (unsaturated soil ), its velocity decreases as soil becomes saturated , and such phenomena is called infiltration. The present model deals with the filt ration of an incompressible fluid (typically, water ) through a porous stratum, the main problem in groundwater infiltration. The present model was developed first by Boussinesq in 1903 and is related to original motivation of Darcy. The mathematical formulation oinfiltration phenomenon leads to a non-linear Boussinesq equation. In the present paper, a numerical solution of Boussinesq e quation has been obtained by using finite differenc e method. The numerical results for a specific set of initial and boundary conditio ns are obtained for determining the height of the fsurface or water mound. The moment infiltrated water enters in unsaturated soil ; the infiltered water will start developing a curv e between saturated porous medium and unsaturated porous medium, which is call ed water table or water mound. Crank-Nicolson finite difference scheme has been applied to obtain the required results for var ious values of time. The obtained numerical results resemble well with the physical phenomena. When water is infiltered through the ve rtical permeable wall in unsaturated porous medium the height of the free surface steadily and uniformly decreases due to the saturat ion of infiltered water as time increases. Forward finite difference scheme is conditionally stable. In the present paper, the gra phical representation shows that Crank-Nicolson fin ite difference scheme is unconditionally stable. Numerical solution of the g overning equation and graphical presentation has be en obtained by using MATLAB coding.