In this article, a local meshless technique is applied for numerical simulation of multi-dimensional Galilei invariant fractional advection–diffusion model on regular and irregular computational domains. In the suggested method, a second-order Crank–Nicolson scheme along with the second-order weighted and shifted Grünwald difference (WSGD) formula, is used to discretize the time derivatives of the model. This time-discretization scheme is unconditionally stable and convergent with order $O\left({\tau }^2\right)$. To approximate the spatial derivatives of this model, a local radial point interpolation technique is employed. Finally, to prove and demonstrate the validity of the proposed algorithm, various one, two and three-dimensional problems are investigated on regular and irregular computational domains.

在本文中，将局部无网格技术应用于规则和不规则计算域上的多维伽利略不变分数对流-扩散模型的数值模拟。在建议的方法中，使用二阶 Crank-Nicolson 方案以及二阶加权和移位 Grünwald 差分 (WSGD) 公式来离散模型的时间导数。这种时间离散化方案是无条件稳定且随阶收敛的$○\left({\tau }^2\right)$. 为了近似该模型的空间导数，采用了局部径向点插值技术。最后，为了证明和证明所提出算法的有效性，在规则和不规则计算域上研究了各种一维、二维和三维问题。