移动粒子半隐式法核函数特征对压力求解稳定性的影响

As a particle-based method, moving particle semi-implicit method (MPS) is widely used for analyzing unsteady flow with free surface. However, a certain degree of pressure fluctuation may occur when solving a specific problem. In this paper, the influence of the shape feature of the kernel function curve on the stability of pressure solution in MPS is analyzed. An exponential polynomial kernel function is constructed, which is verified by a typical static pressure example (hydrostatic pressure problem) and a dynamic pressure example (liquid sloshing problem). Simulation is conducted and the results are compared with the theoretical solution or experimental results. It is found that the improved kernel function can effectively suppress the pressure oscillation in the simulation process. Studies have shown that the shape features of the ratio of the kernel function to the corresponding particle number density can truly reflect the interaction between particles and play a vital role in the analysis of pressure stability. When the improved kernel function is a smooth monotone decreasing non-negative function and its maximum value is a finite value and the value of r/r_e is in the range of [0, 1], gentle change of the numerical values of the kernel function is more conducive to keeping the particle spacing at a reasonable distance, and the pressure solution is more stable. In addition, the value of kernel function near r/r_e=0.8 cannot be too small, otherwise the dynamic performance of the system will be affected.