Modelling coupled density-dependent flow and solute transport with the differential quadrature method
The salt water intrusion phenomenon endangering the groundwater sources, particularly in coastal aquifers, is modeled by the coupled density-dependent flow and solute transport equations. This study focuses on the solution of these interdependent equations by means of the polynomial based Differential Quadrature Method (DQM). The Lagrange interpolation polynomials were selected as basis functions to obtain weighting coefficients for approximating the spatial derivatives and the 4-stage, 4th order Strong Stability Preserving linear Runge Kutta (SSP-RK) algorithm was employed as the time integrator. Two well-known benchmark cases; Henry and Elder problems were examined to test the accuracy and the reliability of the proposed numerical model. Apart from these theoretical benchmark problems, the numerical model was tested with real experimental data from a laboratory-scale study in the literature. The DQM model was observed to provide stable and highly precise results regarding the current semi-analytical and numerical solution schemes.