ABSTRACT Forward–backward solute dispersion with an intermediate point source in one-dimensional semi-infinite homogeneous porous media is studied in this paper. Solute transport under sorption conditions, first-order decay and zero-order production terms are included. The first type of boundary condition is taken as a constant point source at an intermediate point from where forward and backward solute dispersion is examined. The Laplace transform method is adopted to solve the governing equation analytically. All the analytical results are obtained in graphical form to investigate the forward–backward solute transport in porous media for various hydrological input data. The graphical nature of the analytical solution is compared with numerical data taken from existing literature and similar results are obtained. Also, numerical solution of the governing equation is obtained by the Crank-Nicolson finite difference scheme and validated with the analytical solution, which demonstrates good agreement between them. Accuracy of the solution is also observed by using RMSE.

中文翻译：

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半无限地下水系统中前向后向溶质弥散分布研究

摘要 本文研究了一维半无限均质多孔介质中具有中间点源的前向后向溶质弥散。包括吸附条件下的溶质输运、一阶衰减和零阶产生项。第一种类型的边界条件被视为中间点的恒定点源，从这里检查向前和向后的溶质扩散。采用拉普拉斯变换方法解析求解控制方程。所有分析结果都以图形形式获得，以研究多孔介质中各种水文输入数据的前后溶质输运。将解析解的图形性质与从现有文献中获取的数值数据进行比较，并获得了类似的结果。还，控制方程的数值解是通过Crank-Nicolson有限差分格式得到的，并用解析解进行了验证，表明它们之间具有良好的一致性。还可以使用 RMSE 观察解的准确性。