Application of Newton iteration to the numerical solution of variable-density groundwater flow in saturated-unsaturated coastal zones

Abstract

When addressing the question of variable saturation and density groundwater flow in coastal zones, the highly nonlinear system of coupled water-salt equations may deserve more attention. The classical Picard scheme is associated with slow calculation speeds and low precision, which hardly meet the actual needs of users. Here, we developed a new numerical solution for coastal groundwater flow issues based on the Newton scheme and compared the advantages and disadvantages of different numerical methods by analyzing the cases of seawater intrusion. The simulation results indicated that the variable-density effect significantly extends the computation time of the model, but the Newton scheme still has the advantages of computational speed and better convergence compared with the Picard scheme, especially in conditions involving high-frequency and large-amplitude tidal fluctuations, steep aquifer slopes, and a coarse grid. Furthermore, the Newton-Picard method, based on the Newton and Picard schemes, improves the robustness of the Newton solution and optimizes the convergence of the Picard solution. This study has revealed the computational characteristics of the Newton scheme in addressing the issues of coastal variable saturation and density groundwater flow, providing new ideas and insights for numerical solutions to coastal groundwater flow problems.