对MPS法在溃坝模拟中数值压力振荡问题的改进

为探索模拟大变形自由面流体运动的高精度数值计算方法，以溃坝水流运动为例，基于MPS法（Moving Particle Semi-implicit method，移动粒子半隐式法）建立了一个垂向二维改良MPS法数值计算模型。首先，为了改善传统MPS法中存在的自由表面粒子误判以及数值能量耗散问题，提出新的自由表面粒子识别方法和高精度的压力梯度模型。在此基础上，以Lobovsky'等的溃坝物理模型实验为例，探讨不同形式压力泊松方程源项对溃坝冲击压计算精度的影响，提出一个新的源项形式。数值结果分析表明，新自由表面粒子识别方法和高精度压力梯度模型可以有效地减少自由面粒子的误判概率，抑制水流运动计算中的数值能量耗散。而压力计算结果与实验结果的对比表明，所提出的压力泊松方程源项可以有效地减少数值压力震荡的幅度。

Improvements of MPS for reducing numerical pressure oscillation in the dam break simulation

For pursuing an appropriate numerical method for free surface flow with large deformation, a vertical two dimensional corrected MPS numerical model for the simulation of the dam break flow was built based on the Moving Particle Semi-implicit (MPS) method. A new free surface detection method and a highly precise pressure gradient model were proposed to mitigate the issues of particle misrecognition and numerical energy dissipation in the original MPS method. Furthermore, the influence of the source term of pressure Poisson equation on the shocking pressure associated with the dam break flow was discussed by the comparison with the experimental results of Lobovský et al., and then a new form of source term was proposed. The calculated results show that the new free surface detection method and the highly precise pressure gradient model have remarkable effects on the decrease of particle misrecognition as well as numerical energy dissipation. Moreover, the comparisons of the numerical pressure calculation and the experimental result reveal the proposed source term of pressure Poisson equation is useful for the reduction of the numerical pressure fluctuation.