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

Yao，Meng1,2,3; Yu，Shengchao1,4; Li，Hailong1,2,3

2023

10.3389/fmars.2023.1127036

Frontiers in Marine Science   Impact Factor & Quartile

2296-7745

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.

Newton scheme numerical solution Picard scheme saturated-unsaturated coastal zones variable density flow

SCI

English

First ; Corresponding

Environmental Sciences & Ecology ; Marine & Freshwater Biology

Environmental Sciences ; Marine & Freshwater Biology

WOS:001045255600001

FRONTIERS MEDIA SA

2-s2.0-85167822429

Scopus

1.School of Environmental Science and Engineering,Southern University of Science and Technology,Shenzhen,China
2.Guangdong Provincial Key Laboratory of Soil and Groundwater Pollution Control,Southern University of Science and Technology,Shenzhen,China
3.State Environmental Protection Key Laboratory of Integrated Surface Water-Groundwater Pollution Control,School of Environmental Science and Engineering,Southern University of Science and Technology,Shenzhen,China
4.Department of Earth Sciences,The University of Hong Kong,Hong Kong

Yao，Meng,Yu，Shengchao,Li，Hailong. Application of Newton iteration to the numerical solution of variable-density groundwater flow in saturated-unsaturated coastal zones[J]. Frontiers in Marine Science,2023,10.

Yao，Meng,Yu，Shengchao,&Li，Hailong.(2023).Application of Newton iteration to the numerical solution of variable-density groundwater flow in saturated-unsaturated coastal zones.Frontiers in Marine Science,10.

Yao，Meng,et al."Application of Newton iteration to the numerical solution of variable-density groundwater flow in saturated-unsaturated coastal zones".Frontiers in Marine Science 10(2023).