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Accurate approximate semi-analytical solutions to the Boussinesq groundwater flow equation for recharging and discharging of horizontal unconfined aquifers
Journal of Hydrology ( IF 5.9 ) Pub Date : 2019-03-01 , DOI: 10.1016/j.jhydrol.2018.12.057
Mohamed Hayek

Abstract The Boussinesq equation is usually used to describe one-dimensional unconfined groundwater movement. Solutions of this equation are important as they provide useful insights regarding the water table response to stream level variations and allow us to quantify the exchange flow between the stream and the aquifer. Due to the nonlinearity of the Boussinesq equation, the solutions are generally obtained using numerical methods. However, for certain classes of initial and boundary conditions there are both exact and approximate analytical solution techniques. This work focuses on the latter approach. A new mathematical technique for approximate solutions of the Boussinesq equation describing flow in horizontal unconfined aquifers induced by sudden change in boundary head is presented. The method applies to the problems of recharging and dewatering of an unconfined aquifer, and approximate solutions to both problems are derived. The solutions were obtained by introducing an empirical function with four parameters which might be obtained using a numerical fitting procedure. Results based on this technique were found to be easily calculated and to be in good agreement with those obtained using numerical calculation based on Runge-Kutta approach. A benchmark between the proposed solutions and five existing approximate analytical solutions shows that the present solutions are the most accurate approximate solutions among those tested. Applications of the solutions are presented in the context of estimating aquifer hydraulic parameters.

中文翻译:

用于水平无承压含水层补给和排放的 Boussinesq 地下水流动方程的精确近似半解析解

摘要 Boussinesq方程常用于描述一维无侧限地下水运动。这个方程的解很重要,因为它们提供了关于地下水位对河流水位变化的响应的有用见解,并使我们能够量化河流和含水层之间的交换流量。由于 Boussinesq 方程的非线性,通常使用数值方法获得解。然而,对于某些类别的初始和边界条件,有精确和近似解析解法技术。这项工作侧重于后一种方法。提出了一种新的数学方法,用于近似解描述边界水头突然变化引起的水平无承压含水层中的流动的 Boussinesq 方程。该方法适用于无承压含水层的补给和脱水问题,并推导出了这两个问题的近似解。这些解是通过引入一个具有四个参数的经验函数来获得的,这些参数可以使用数值拟合程序获得。发现基于这种技术的结果很容易计算,并且与使用基于 Runge-Kutta 方法的数值计算获得的结果非常吻合。所提出的解与五个现有近似解析解之间的基准表明,当前的解是测试中最准确的近似解。在估计含水层水力参数的背景下介绍了这些解决方案的应用。这些解是通过引入一个具有四个参数的经验函数来获得的,这些参数可以使用数值拟合程序获得。发现基于这种技术的结果很容易计算并且与使用基于 Runge-Kutta 方法的数值计算获得的结果非常一致。所提出的解与五个现有近似解析解之间的基准表明,当前的解是测试中最准确的近似解。在估计含水层水力参数的背景下介绍了这些解决方案的应用。这些解是通过引入一个具有四个参数的经验函数来获得的,这些参数可以使用数值拟合程序获得。发现基于这种技术的结果很容易计算,并且与使用基于 Runge-Kutta 方法的数值计算获得的结果非常吻合。所提出的解与五个现有近似解析解之间的基准表明,当前的解是测试中最准确的近似解。在估计含水层水力参数的背景下介绍了这些解决方案的应用。发现基于这种技术的结果很容易计算,并且与使用基于 Runge-Kutta 方法的数值计算获得的结果非常吻合。所提出的解与五个现有近似解析解之间的基准表明,当前的解是测试中最准确的近似解。在估计含水层水力参数的背景下介绍了这些解决方案的应用。发现基于这种技术的结果很容易计算,并且与使用基于 Runge-Kutta 方法的数值计算获得的结果非常吻合。所提出的解与五个现有近似解析解之间的基准表明,当前的解是测试中最准确的近似解。在估计含水层水力参数的背景下介绍了这些解决方案的应用。
更新日期:2019-03-01
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