In this study, we propose a new numerical method, which can be effectively applied to the advection-dispersion equation, based on B-spline functions and method of lines approach. In the proposed approach, spatial derivatives are calculated using quintic B-spline functions. Thanks to the method of lines approach, the partial differential equation governing the contaminant transport in groundwater is converted into time-dependent ordinary differential equations. After this transformation, the time-integration of this system is realized by using an adaptive Runge–Kutta formula. In order to test the accuracy of the proposed method, four numerical examples were solved and the obtained results compared with various analytical and numerical solutions given in the literature. It is proven that the proposed method is faster and more reliable than other methods referenced herein and is a good alternative for simulation of contaminant transport problems as a result of these comparisons.

中文翻译：

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用于模拟地下水中污染物迁移的线的 B 样条方法

在这项研究中，我们提出了一种新的数值方法，它可以有效地应用于对流 - 弥散方程，基于 B 样条函数和线方法。在所提出的方法中，使用五次 B 样条函数计算空间导数。由于采用线法方法，控制地下水中污染物运移的偏微分方程被转化为随时间变化的常微分方程。经过这种转换，该系统的时间积分是通过使用自适应 Runge-Kutta 公式实现的。为了测试所提出方法的准确性，求解了四个数值例子，并将所得结果与文献中给出的各种解析解和数值解进行了比较。