In the current work, an efficient and powerful computational technique is implemented to simulate an anomalous mobile-immobile solute transport process. The process is mathematically modelled as a time-fractional mobile-immobile diffusion equation in the sense of Riemann-Liouville derivative. Firstly, an implicit time integration procedure is used to semi-discretize the model in the time direction. The unconditional stability of the proposed time discretization scheme has been proven. Then an adaptive sparse meshless method has been formulated and implemented to fully discretize the model. In this approach, a kernel-based collocation method is equipped with a greedy sparse approximation procedure to discretize the governing problem on a convenient neighborhood of each data point with acceptable accuracy. Therefore, it leads to a sparse and well-conditioned algebraic system. Some test problems on regular and irregular computational domains are presented to verify the validity, efficiency, and accuracy of the method.

在当前的工作中，实现了一种有效而强大的计算技术，以模拟异常的移动-不移动溶质传输过程。在黎曼-利维尔导数的意义上，该过程在数学上被建模为时间分数阶移动-固定扩散方程。首先，使用隐式时间积分过程在时间方向上对模型进行半离散化。已经证明了所提出的时间离散方案的无条件稳定性。然后，提出并实施了一种自适应稀疏无网格方法，以使模型完全离散。在这种方法中，基于内核的搭配方法配有贪婪的稀疏近似过程，可以在每个数据点的方便邻域上以可接受的精度离散控制问题。因此，它导致了稀疏且条件良好的代数系统。提出了在规则和不规则计算域上的一些测试问题，以验证该方法的有效性，效率和准确性。