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Mathematical modeling for solute transport in aquifer

机译:含水层中溶质运移的数学模型

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Groundwater pollution may occur due to human activities, industrial effluents, cemeteries, mine spoils, etc. This paper deals with one-dimensional mathematical modeling of solute transport in finite aquifers. The governing equation for solute transport by unsteady groundwater flow is solved analytically by the Laplace transform technique. Initially, the aquifer is subjected to the spatially dependent source concentration with zero-order production. One end of the aquifer receives the source concentration and is represented by a mixed-type boundary condition in the splitting time domain. The concentration gradient at the other end of the porous media is assumed to be zero. The temporally dependent velocity and the dispersion coefficients are considered. A numerical solution is obtained by using an explicit finite difference scheme and compared with the analytical result. Accuracy of the solution is discussed by using the root mean square error method. Truncation error is also explored for the parameters like numerical dispersion and velocity terms. The impact of Peclet number is examined. For graphical interpretation, unsteady velocity expressions (i.e., such as exponential, sinusoidal, asymptotic, and algebraic sigmoid) are considered. The work may be used as a preliminary predictive tool for groundwater resource and management.
机译:地下水污染可能是由于人类活动,工业废水,墓地,矿渣等引起的。本文研究了有限含水层中溶质运移的一维数学模型。用拉普拉斯变换技术解析地解决了不稳定地下水流中溶质运移的控制方程。最初,含水层受到零级产量的空间相关源浓度的影响。含水层的一端接收到源的浓度,并由分裂时域中的混合类型边界条件表示。多孔介质另一端的浓度梯度假定为零。考虑了时间相关的速度和色散系数。通过使用显式有限差分方案获得数值解,并将其与分析结果进行比较。通过使用均方根误差方法来讨论解决方案的准确性。还研究了诸如数字弥散和速度项之类的参数的截断误差。检查佩克利特数的影响。为了进行图形解释,考虑了非定常速度表达式(即指数,正弦,渐近和代数S形)。这项工作可以用作地下水资源和管理的初步预测工具。

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