移动粒子半隐式法核函数特征对压力求解稳定性的影响

Influence of the Kernel Function Characteristics on the Stability of Pressure Solution of Moving Particle Semi-Implicit Method

针对移动粒子半隐式法在求解特定问题时,压力求解可能会出现一定程度的波动,分析了移动粒子半隐式法中核函数曲线形状特征对压力求解稳定性的影响,构造了一种指数多项式型核函数。模拟了典型静压(静水压力问题)和动压(液体晃动问题)算例,并将模拟结果与理论解或实验值进行对比,研究结果表明:改进的核函数可有效抑制模拟过程中压力求解的振荡现象;核函数与对应粒子数密度比值曲线的形状特征可真实反映粒子间相互作用关系,在稳定性分析中起着至关重要的作用。当核函数是光滑单调递减非负函数且最大值为有限值、两粒子间距离与影响半径的比r/re在[0,1]区间时,曲线两端附近核函数数值变化平缓更有利于使粒子保持合理距离,压力求解更加稳定;在r/re为0.8的附近,核函数值过小时会影响系统的动力学性能。

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.