粒子法中压力振荡的机理研究

移动粒子半隐式法(moving particle semi-implicit method, MPS)是一种适用于不可压缩流体的无网格方法, MPS方法常应用于自由表面大变形问题.MPS 方法提出至今一直存在着严重的压力振荡问题. 本研究针对MPS 方法中存在的压力振荡现象, 首先将实际的物理问题简化为一维模型, 并从粒子之间相互位置关系的角度说明了MPS 方法中压力波动产生的原因.在采用MPS方法进行模拟时, 加入了粒子碰撞模型, 通过对碰撞系数的选择从而控制粒子之间的相互位置关系.并且对经典的溃坝问题进行了模拟, 结果表明随着碰撞系数的增加, 粒子数密度偏差的波动幅度都会减小, 从而压力振荡的幅度得到了有效的抑制.并且对比了两种不同核函数对压力振荡的影响, 结果表明: 采用高斯核函数时, 压力振荡的幅度更小, 这是因为采用高斯核函数时, 相同的粒子位置波动幅度将会得到较小的粒子数密度偏差的波动.由于在模拟过程中粒子运动的随机性, 这将导致粒子数密度偏差产生随机的波动, 从而产生压力振荡, 因此粒子法中的压力振荡很难彻底消除. 

MECHANISM ANALYSIS OF PRESSURE OSCILLATION IN PARTICLE METHOD

The moving particle semi-implicit method was developed to simulate incompressible fluid using a meshless method. There was a big problem that the space distribution and the time variation of pressure oscillate drastically in the MPS method. In order to investigate the pressure oscillation in the MPS method, the simplified one-dimensional model was developed. The mechanism of pressure oscillation in the MPS method was illustrated by the movement and the relative position between the center particle and its neighbor particles. The collision model was employed in the simulation and the relative position between particles was controlled by choosing different collision parameters. The classical dam break problem was simulated. With the increase of collision parameter, the fluctuation of the deviation of particle number density decreased. According, the amplitude of pressure oscillation was suppressed. Two different kernel functions were also employed to investigate the pressure oscillations. The results showed that the gauss kernel function improved the stabilization of pressure calculation. It was the reason that the same movement of particles lead to less deviation of particle number density when the gauss kernel function was used. And the randomness of particles motion led to random fluctuation in the deviation of particle number density. As a result, the pressure fluctuation in MPS method occurred and it was difficult to be eliminated.