基于Trefftz法的沿海越流含水层系统地下水研究

本文提出使用Trefftz法结合时空配点法建立沿海越流含水层系统承压地下水暂态模型的首创性研究。本文利用分离变量推导了越流含水层地下水控制方程的Trefftz基底,并通过叠加以获得满足控制方程的近似解。基于时空坐标系统,求解越流含水层系统承压地下水的暂态流动情况。本文运用该方法将数值解与解析解进行对比和精度研究,结果证明了Trefftz法研究越流含水层系统地下水的可行性。此后,进一步针对沿海地下水进行数值模拟,并与有限差分法进行比较分析,结果不仅准确地描绘了地下水波动特征,更加表明了Trefftz法在沿海越流含水层系统地下水研究的适用性。

Study on groundwater in coastal leakage aquifer system based on the Trefftz method

This paper proposes a groundbreaking study of establishing a transient model of confined groundwater in a coastal aquifer system using the Trefftz method combined with the space-time collocation method. In this paper, the Trefftz basis of the governing equation of groundwater in leakage aquifer is derived by separation of variables, and an approximate solution that satisfies the governing equation is obtained by superposition. Based on the space-time coordinate system, the transient flow of confined groundwater in the aquifer system is solved. In this paper, the method is used to compare the numerical solution with the analytical solution and study the accuracy. The result proves that the Trefftz method is feasible to study the groundwater in the aquifer system. Since then, further numerical simulations of coastal groundwater have been carried out and compared with the finite difference method. The results not only accurately describe the characteristics of groundwater fluctuations, but also demonstrate the applicability of Trefftz method for groundwater research in coastal leakage aquifer systems.