Water Level Correction and Streamline Tracing in Phreatic Aquifer Pumping Well Flow Simulation Using Finite Difference Method
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摘要:
中心网格有限差分法模拟水位与流线是开展众多水文地质工作的基础.为了解决潜水含水层中抽水井处水位模拟误差问题并精确识别流线.本研究基于复势理论，推导了中心网格有限差分法抽水井处水位校正公式，耦合数值模型量化分析了水位校正对流线精度的影响.结果表明，校正公式可显著提升抽水井处水位模拟精度；同时明确了当离散网格尺寸约为井半径的5倍时，无需校正即可同时保证水位与流线的模拟精度.该研究为解决数值模拟中离散化带来的模拟误差提供了理论依据与实用判据.
Abstract:Block-centered finite difference method for simulating water levels and streamlines is the basis of numerous hydrogeological works. To address the simulation error of water levels at pumping wells in a phreatic aquifer and accurately identify streamlines, this study derives a water level correction fomula for pumping wells in the block-centered finite difference method based on complex potential theory. A coupled numerical model is developed to quantitatively analyze the impact of water level correction on the accuracy of streamlines. The results demonstrate that the correction formula significantly improves the simulation accuracy of water levels at pumping wells. Furthermore, it is clarified that when the discrete grid size is approximately 5 times the well radius, both water level and streamline simulation accuracy can be ensured without the need for correction. This study provides a theoretical basis and practical criterion for mitigating simulation errors caused by discretization in numerical modeling.
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Key words:
- block-centered finite difference /
- phreatic aquifer /
- pumping well /
- water level /
- streamline /
- environmental geology
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图 1 抽水井所在网格与周边网格格点编号示意
Fig. 1. Node numbers for the pumping well cell and surround grid cells
图 2 MODPATH井上粒子追踪起点分布示意
Fig. 2. Starting point distribution for particle tracking on the well rim in MODPATH
图 5 抽水井处水位模拟值、校正值与真实值对比
Fig. 5. Comparison of simulated, calibrated, and analytical water levels on the pumping well rim
图 6 案例B的流线模拟结果
a.流场真实解；b.ΔX=200 m；c.ΔX=0.32 m；d.X=-10 000 m时，分界线纵坐标Y的模拟值与真实解对比
Fig. 6. Streamline simulation results for case B
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