无网格SPH法中守恒光滑法的修正

Correction of conservative smoothing approach used in SPH method

守恒光滑法CSA(Conservative Smoothing Approach)是解决传统SPH(Smoothed Particle Hydrodynamics)法稳定性问题的一种很有效的方法.研究发现在SPH法中运用所谓的守恒光滑法并不能保证系统的总物理量(质量、动量或者能量)在每个时间步均守恒,而是随着时间在理论值附近波动,对计算结果的精度有一定的影响.对此提出了守恒光滑法的修正公式,对SPH控制方程得到的各个粒子的物理量进行CSA光滑,然后运用文中提出的CSA的修正公式把对该粒子物理量的改变量加权平均给邻域内各个粒子,从而确保了SPH算法中系统的总物理量(质量、动量以及能量等)在每个时间步均守恒,而且由于减少了CSA对SPH得到的各个粒子物理量的过分光滑,从而提高了计算精度.物理意义、理论推导以及文中的算例均证明了这种修正的有效性.

The conservative smoothing approach（CSA） is a kind of methods which is very efficient for eliminating the instability of traditional smoothed particle hydrodynamics（SPH） method.Research discovered that total physical quantities of system（such as mass,moment and energy） were no longer strictly conservative in each time step with the use of CSA.The calculated value fluctuated around the theoretical value with time and affected the result precision.Correction of CSA（CCSA） was proposed.Used CSA to smooth the physical variables obtained from SPH governing equations and then used CCSA to weighted average the change of the physical variables to each neighbor node,thus ensured the conservation of total physical quantities of system（such as mass,moment or energy） in each time step.Owing to reduce of the excessive smoothness which CSA acted on physical variables,calculation accuracy was improved.Physical meaning,theoretical derivation and numerical test show the efficiency of this correction.