The pollution propagation within the underground water reservoirs is a challenging and important phenomenon. In the current work, the numerical simulation of pollution transport in an underground channel is performed using the meshless method. To account the anomalous dispersion in a general case, the variable order fractional mass transfer equation is utilized for a rectangular channel. The clean fluid stream enters the channel and due to several phenomenon including the leakage of pollution from the channel walls, the internal pollution source, and the occurrence of the chemical reactions, the pollution content is affected. The non-dimensional form of the governing equation is derived to introduce the dominant dimensionless group numbers. The numerical solution of the obtained equation is established based on the meshless local Petrov–Galerkin method using the moving Kriging interpolation. The Dirac delta function is used as a test function over the local sub-domains. To discretize the present formulation in space variables, we apply the moving Kriging shape functions. Also, to estimate the fractional-order versus the time, finite difference relation is utilized. Using Kronecker’s delta property of moving Kriging interpolation shape functions the boundary conditions in the final system are imposed automatically. The main aim of this technique is to investigate a global estimation for the model, which consequently decrease such problems to those of solving a system of algebraic equations. To determine the accuracy and efficiency of the present method on regular and irregular domains, an example is given in various domains and with regular and irregular distributed points. Also, the effect of major parameters including the fractional order exponent, leakage velocity, chemical reaction rate constant, diffusion coefficient in addition to the stationary/moving pollution source is also examined. It will be shown that, by enhancement of the diffusivity from 0.1 to 20, the outlet concentration reduces by 25.1%, while diffusivity increase from 20 to 50 affects the exiting pollution by merely 7.0%.

地下水库内的污染传播是一个具有挑战性和重要的现象。在目前的工作中，使用无网格方法对地下通道中的污染物传输进行了数值模拟。为了说明一般情况下的异常色散，对矩形通道使用变阶分数传质方程。干净的流体流进入通道，由于通道壁的污染泄漏、内部污染源和化学反应的发生等多种现象，污染含量受到影响。推导出控制方程的无量纲形式以引入主要的无量纲群数。基于无网格局部 Petrov-Galerkin 方法，使用移动克里金插值法建立了所得方程的数值解。Dirac delta 函数用作本地子域上的测试函数。为了在空间变量中离散当前公式，我们应用移动克里金形状函数。此外，为了估计分数阶与时间的关系，使用了有限差分关系。使用 Kronecker 的移动克里金插值形状函数的 delta 属性，自动施加最终系统中的边界条件。该技术的主要目的是研究模型的全局估计，从而将此类问题减少到求解代数方程组的问题。为了确定本方法在规则和不规则域上的准确性和效率，在各种域中以及具有规则和不规则分布点的示例中给出。此外，除固定/移动污染源外，还研究了主要参数的影响，包括分数阶指数、泄漏速度、化学反应速率常数、扩散系数。结果表明，通过将扩散系数从 0.1 提高到 20，出口浓度降低了 25.1%，而扩散系数从 20 增加到 50，对出口污染的影响仅为 7.0%。除了固定/移动污染源外，还检查了扩散系数。结果表明，通过将扩散系数从 0.1 提高到 20，出口浓度降低了 25.1%，而扩散系数从 20 增加到 50，对出口污染的影响仅为 7.0%。除固定/移动污染源外，还检查了扩散系数。结果表明，通过将扩散系数从 0.1 提高到 20，出口浓度降低了 25.1%，而扩散系数从 20 增加到 50，对出口污染的影响仅为 7.0%。