simulation of fingering phenomena in fluid flow through fracture porous media with inclination and gravitational effect

Here we have studied the fingering phenomena in fluid flow through fracture porous media with inclination and gravitational effect and investigate the applicability of adomian decomposition method to the nonlinear partial differential equation arising in this phenomena and prove the convergence of adomian decomposition scheme, which leads to an abstract result and an analytical approximate solution to the equation. finally developed a simulation result of saturation of wetting phase with and without considering the inclination effect for some interesting choices of parametric data value and studied the recovery rate of the oil reservoir with dimensionless time.