Numerical analysis of groundwater flow problems by differential quadrature method

Within the scope of this study, in addition to traditional solution methods such as finite differences, finite elements and boundary elements in the numerical solution of groundwater flow problems, it is aimed to introduce the new and developing Differential Quadrature Method (DQM) and to apply it to groundwater flow problems. In the study, one and two-dimensional groundwater flow problems were examined, and the numerical calculation of spatial derivatives using the DQM method was investigated by using various nodal point distributions according to the preferred polynomial approach. In time-dependent one and two-dimensional groundwater flow problems, it is aimed to convert the time-dependent partial differential equation to an ordinary differential equation system with the Method of Lines (MOL) for the calculation of temporal derivatives. The resulting ordinary differential equation systems were solved numerically using different time schemes. The method was first applied to the modeling of a one-dimensional confined aquifer. Since there was no analytical solution here, the accuracy of the model results was investigated with reference solutions. In the second problem, the modeling of two-dimensional steady-state groundwater flow with known analytical solutions was performed. Finally, the current method was applied to one- and two-dimensional unsteady-state pollutant transport problems with known analytical solutions. The numerical results obtained were compared with analytical and literature solutions. When the performance of the method is examined as a result of the comparisons, it is revealed that it produces efficient and high-accuracy solutions with minimum computational effort.