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Analytical and numerical solutions to describe water table fluctuations due to canal seepage and time-varying recharge
Journal of Hydroinformatics ( IF 2.2 ) Pub Date : 2022-07-01 , DOI: 10.2166/hydro.2022.037
Ashutosh Upadhyaya 1 , Manisha M. Kankarej 2
Affiliation  

Hybrid finite analytic solution (HFAS), Galerkin's method based finite element solution (FES) and fully implicit finite difference solution (FIFDS) of one dimensional nonlinear Boussinesq equation and Analytical solution of Boussinesq equation linearized by Baumann's transformation (analytical solution I, AS I) as well as linearized by Werner's transformation (analytical solution II, AS II) were employed to obtain water table rise in a horizontal unconfined aquifer lying between two canals located at finite distance having different elevations and subjected to various patterns of recharge, i.e. zero recharge, constant recharge, as well as time varying recharge. Considering HFAS as benchmark solution, water table in mid region as obtained from FES followed by FIFDS was observed quite close to that obtained from HFAS and as per L2 and Tchebycheff norms computation, it was ranked at first and second place, respectively. Both AS I and AS II predicted higher water table at t = 5 days but at t = 10 days, AS I predicted lower and AS II predicted higher water table at all distances due to linearization effect. So, analytical solutions of linearized Boussinesq equation were rated lower than numerical solutions of nonlinear Boussinesq equation.



中文翻译:

用于描述由于渠道渗漏和时变补给引起的地下水位波动的分析和数值解

一维非线性Boussinesq方程的混合有限解析解(HFAS),基于Galerkin方法的有限元解(FES)和完全隐式有限差分解(FIFDS)和Baumann变换线性化的Boussinesq方程的解析解(解析解I,AS I)以及通过 Werner 变换(解析解 II,AS II)进行线性化,以获取水平无承压含水层中的地下水位上升,该含水层位于位于有限距离、具有不同海拔的两条运河之间,并受到各种补给模式,即零补给,持续充电,以及随时间变化的充电。考虑 HFAS 作为基准解决方案,从 FES 和 FIFDS 获得的中部地区地下水位与从 HFAS 获得的水位非常接近,根据 L2 和 Tchebycheff 范数计算,它分别排名第一和第二位。AS I 和 AS II 都预测在t = 5 天,但在t = 10 天,由于线性化效应,AS I 预测的地下水位较低,AS II 预测所有距离的地下水位较高。因此,线性化 Boussinesq 方程的解析解被评为低于非线性 Boussinesq 方程的数值解。

更新日期:2022-07-01
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