Comparison study of artificial recharge of an unconfined aquifer with limited lateral extent

摘要

A rechearge well-unconfined aquifer system is considered with limited lateral extent. The physical problem is described by the non linear Bounssinesq equation, written in cylindrical coordinates and is characterized by the validity of the Dupuit-Forcheimer assumptions and proper boundaries conditions. Dimensional analysis is used to transform the established equation, which is linearized by a sepecial linearization technique. Both equations, the linearized and the non linear, are solved by the Crank-Nicholson finite-differnce computational scheme. The numerical results of boith solutions are compared with a semi-analytical solution arising by the method of successive variations of steady states. The semi-analytical solution closely approximates both numerical solutions, which asymptotically attain the same equation of steady flow. Computationally both methods are inherently stable for any time. So the special linearization technique used. simplifies the non linear problem and approximates closely the non linear solution.