An easy implemented and effective pure meshfree method is first developed to solve the 1D/2D constant/variable-order time fractional convection-diffusion equation (TF-CDE) on non-regular domain with two boundary conditions in this paper. The proposed method (CSPH-FDM) is derived from that the finite difference scheme (FDM) for Caputo time fractional derivative and a corrected smoothed particle hydrodynamics (CSPH) without kernel derivative for spatial derivatives. In the proposed CSPH-FDM, the high-order spatial derivative is divided into multi first-order derivatives and solved continuously by the CSPH, the Neumann boundary condition can be accurately treated, the two distribution cases of the local refinement and irregular particles or the arbitrary irregular shape domain can be easily and effectively implemented by the CSPH. To demonstrate the validity and numerical convergent order of the proposed method, several 1D/2D analytical examples with local refinement and irregular particles distributions or on complex geometries are first investigated, in which a four-order derivate problem with Neumann boundary is also considered. Subsequently, the CSPH-FDM is extended to predict the solute moving process versus time by two TF-CDEs on different irregular domains and compared with other numerical results. All the numerical results show the flexible application ability and reliability of the present method.

本文首先提出了一种简单易行且有效的纯无网格方法，以求解带有两个边界条件的非规则域上的一维/二维维数/定阶时间分数对流扩散方程（TF-CDE）。提出的方法（CSPH-FDM）源自Caputo时间分数导数的有限差分方案（FDM）和空间导数的无核导数的校正平滑粒子流体动力学（CSPH）。在所提出的CSPH-FDM中，高阶空间导数被分为多个一阶导数，并由CSPH连续求解，可以精确地处理Neumann边界条件，局部细化和不规则粒子的两种分布情况或CSPH可以轻松有效地实现任意不规则形状域。为了证明该方法的有效性和数值收敛阶，首先研究了几个具有局部细化和不规则粒子分布或在复杂几何形状上的一维/二维分析实例，其中还考虑了具有Neumann边界的四阶导数问题。随后，CSPH-FDM扩展为通过在不同不规则区域上的两个TF-CDE预测溶质移动过程随时间的变化，并与其他数值结果进行比较。所有数值结果表明，该方法具有灵活的应用能力和可靠性。其中还考虑了具有Neumann边界的四阶导数问题。随后，CSPH-FDM被扩展以通过两个不规则区域上的两个TF-CDE预测溶质移动过程随时间的变化，并与其他数值结果进行比较。所有数值结果表明，该方法具有灵活的应用能力和可靠性。其中还考虑了具有Neumann边界的四阶导数问题。随后，CSPH-FDM扩展为通过在不同不规则区域上的两个TF-CDE预测溶质移动过程随时间的变化，并与其他数值结果进行比较。所有数值结果表明，该方法具有灵活的应用能力和可靠性。