Numerical Modeling Based on Implicit Differential Quadrature Method for Two-Dimensional Groundwater Flow Problems

Predicting the behavior of fluid flow through the porous media is significantly important, especially in arid and semi-arid regions. In the present research, a novel numerical model based on the Implicit Differential Quadrature Method (IDQM) was developed to simulate the two-dimensional groundwater flow problems with the nonlinear Boussinesq equation. The data of the grid points were calculated from Chebyshev–Gauss–Lobatto formula. To evaluate the accuracy and the efficiency of the suggested model, three commonly reported in the literature groundwater problems were employed: (i) a problem related to the Boussinesq equation with an analytical solution, (ii) a hypothetical case of groundwater flow problem in a confined aquifer, and (iii) an aquifer pumping test. In addition, the results of the above-mentioned model were compared with the numerical predictions of the explicit and implicit schemes of the finite difference method (EFDM and IFDM). The findings demonstrated high accuracy, efficiency, and superiority of the numerical results of the IDQM. According to the results, the lowest values of  root mean square error (RMSE) in the first, second, and third test cases with a range of (2.83E-23-5.65E-12), (0.072-0.065), and (0.230-0.100) were observed using IDQM. The values of dimensionless differences (DD) were also assigned the lowest values in this method in all tests. Briefly, the IDQM using less number of nodes provided more accurate results than EFDM and IFDM and as a result, is applicable to a wide range of problems in numerous fields of science and engineering.