When a smoothed particle hydrodynamics (SPH) method, a Lagrangian and meshfree numerical scheme, is used to solve the advection-dispersion equation (ADE), SPH solutions may not be accurate when particles are irregularly distributed, i.e., the distance between two neighbor particles varies irregularly in a simulation domain. Particle irregularity may be caused by nonuniform groundwater flow in a heterogeneous field of hydraulic conductivity. This study explores for the first time whether the Finite Particle Method (FPM) can provide more accurate ADE solutions than SPH does for irregularly distributed particles. FPM is similar to SPH in theory, but uses a modified kernel gradient to construct a SPH approximation of solute concentration gradients. Performance of SPH and FPM with irregularly distributed particles is evaluated by using two numerical cases. The first case considers only diffusive transport, and has an analytical solution for the evaluation. The second case considers both advection and dispersion, and uses a numerical solution as a reference for the evaluation. For each of the two cases, several numerical experiments are conducted using multiple sets of irregularly distributed particles with different levels of particle irregularity due to different levels of heterogeneity of hydraulic conductivity. Numerical results indicate that, for the numerical experiments of this study, FPM outperforms SPH to yield more accurate ADE solutions. However, FPM solutions are still subject to numerical errors, and the errors increase when the level of heterogeneity of hydraulic conductivity increases. Further improvement of FPM is warranted in a future study.

当使用平滑粒子流体动力学 (SPH) 方法（一种拉格朗日和无网格数值方案）求解对流-弥散方程 (ADE) 时，当粒子不规则分布时，即两个相邻粒子之间的距离，SPH 解可能不准确在模拟域中不规则地变化。颗粒不规则可能是由于水力传导率异质领域中不均匀的地下水流造成的。本研究首次探讨了有限粒子法 (FPM) 是否可以为不规则分布的粒子提供比 SPH 更准确的 ADE 解决方案。FPM 在理论上类似于 SPH，但使用修改后的内核梯度来构建溶质浓度梯度的 SPH 近似值。SPH 和 FPM 具有不规则分布的粒子的性能通过使用两个数值案例进行评估。第一种情况只考虑扩散传输，并有一个用于评估的解析解。第二种情况同时考虑对流和弥散，并使用数值解作为评估的参考。对于这两种情况中的每一种，都使用多组不规则分布的颗粒进行了几次数值实验，这些颗粒由于水力传导率的不均匀程度不同而具有不同程度的颗粒不规则性。数值结果表明，对于本研究的数值实验，FPM 优于 SPH 以产生更准确的 ADE 解。然而，FPM 解仍然存在数值误差，并且随着导水率非均质性水平的增加，误差增加。在未来的研究中需要进一步改进 FPM。