A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function

In this study, we have obtained numerical solutions for non-Darcian flow to a well with the finite difference method on the basis of the Izbash equation, which states that the hydraulic gradient is a power function of the specific discharge. The comparisons between the numerical solutions and the Boltzmann solutions and linearization solutions have also been done in this study. The results indicated that the linearization solutions for both the infinitesimal-diameter well and the finite-diameter well agree very well with the numerical solution at late times, while the linearization method underestimates the dimensionless drawdown at early and moderate times. The Boltzmann method works well as an approximate analytical solution for the infinitesimal-diameter well. Significant differences have been found between the Boltzmann solution for a finite-diameter well and the numerical solution during the entire pumping period. The analysis of the numerical solution implies that all the type curves inside the well for different dimensionless non-Darcian conductivity kD values approach the same asymptotic value at early times, while a larger kD leads to a smaller drawdown inside the well at late times. A larger kD results in a larger drawdown in the aquifer at early times and a smaller drawdown in the aquifer at late times. Flow approaches steady-state earlier when kD is larger.