Abstract The fractal mobile/immobile model of the solute transport is based on the assumption that the waiting times in the immobile region follow a power-law, and this leads to the application of fractional time derivatives. The model covers a wide family of systems that include heat diffusion and ocean acoustic propagation. This paper develops an efficient computational technique, stemming from the radial basis function-generated finite difference (RBF-FD), to solve the fractal mobile-immobile transport model (FMTM). The time fractional derivative of the FMTM is discretized via the shifted Grunwald-Letnikov formula with second-order accuracy. On the other hand, the spatial derivative is approximated using the local RBF-FD method. The main benefit of the local collocation technique is that we only need to consider discretization points present in each of the sub-domains around the collocation point. The stability and convergence analysis of the proposed method are proven via the energy method in the L2 space. The numerical results for the FMTM on regular and irregular domains confirm the theoretical formulation and efficiency of the proposed scheme.

中文翻译：

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多孔和断裂介质中分形移动/固定输运模型的数值模拟方法

摘要 溶质运移的分形移动/不动模型基于不动区域的等待时间遵循幂律的假设，这导致了分数时间导数的应用。该模型涵盖了广泛的系统系列，包括热扩散和海洋声学传播。本文开发了一种源自径向基函数生成有限差分 (RBF-FD) 的高效计算技术，以解决分形移动-固定传输模型 (FMTM)。FMTM 的时间分数阶导数通过具有二阶精度的移位 Grunwald-Letnikov 公式进行离散化。另一方面，使用局部 RBF-FD 方法来近似空间导数。局部搭配技术的主要好处是我们只需要考虑在搭配点周围的每个子域中存在的离散化点。通过L2空间中的能量方法证明了所提出方法的稳定性和收敛性分析。FMTM 在规则域和不规则域上的数值结果证实了所提出方案的理论公式和效率。