From the previous works, we found that the stability of the pressure solution obtained by using particle-based method can be improved by solving the pressure equation on a stationary Eulerian grid. In this study, the Multiquadric Radial Basis Function (RBF-MQ) interpolation technique is applied for the data transfer between Lagrangian particles and Eulerian grids in solving the incompressible Navier-Stokes equations. Also, the argument on selecting the optimal shape parameter (for MQ kernel) is resolved in the current work as well by using the information of the surrounding nodes. In order to preserve the continuity constraint on the particle level, the divergence-free interpolation scheme is proposed to interpolate the velocity from grid to particle. For validation purpose, a series of flow cases are solved by using the current Moving Particle with Pressure Mesh (MPPM) method and good agreement has been found between the current and the benchmark solutions. Also, we found that the current method is more accurate than our previous MPPM method.

从以前的工作中，我们发现通过在固定的欧拉网格上求解压力方程可以提高使用基于粒子的方法获得的压力溶液的稳定性。在这项研究中，采用多元二次径向基函数（RBF-MQ）插值技术来求解拉格朗日粒子与欧拉网格之间的数据传递，从而解决了不可压缩的Navier-Stokes方程。另外，在当前工作中，也通过使用周围节点的信息来解析有关选择最佳形状参数（用于MQ内核）的参数。为了保持对粒子水平的连续性约束，提出了无散度插值方案来对网格到粒子的速度进行插值。出于验证目的，使用当前的带有压力网格的移动粒子（MPPM）方法解决了一系列流动情况，并且在当前解决方案和基准解决方案之间找到了很好的协议。此外，我们发现当前方法比以前的MPPM方法更准确。