摘要
光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法在模拟大变形问题时具有明显的优势,但是由于粒子的不连续性,致使其计算精度较低。文中对光滑粒子流体动力学方法中函数及其一阶导数的核估计进行详细研究。讨论传统的SPH方法和改进的CSPH(corrective smoothed particle hydrodynamics)方法的离散思想,在Taylor展开的基础上引入修正的MSPH(modified smoothed particle hydrodynamics)方法,并推导一维和二维情况下函数的核估计和函数的一阶导数核估计的离散形式。最后通过数值算例,对三种不同的SPH方法的计算精度进行详细比较,结果表明,CSPH和MSPH方法可以极大提高边界粒子的计算精度,在二维情况下,MSPH方法的计算精度要优于CSPH方法。
Smoothed particle hydrodynamics （SPH） is an effective method for modeling problems involving large deformation. However, particle inconsistency can lead to low accuracy. The kernel function estimation and its first derivative estimation are investigated in the smoothed particle hydrodynamics method. The discrete scheme of the conventional and the corrective SPH （CSPH） methods are introduced. Based on Taylor series expansion, modified SPH （MSPH） method is proposed. The discrete forms of the function and the first derivative estimations of the kernel function are deduced in both one and two dimensional space. Then several numerical examples are carried out to compare the accuracy of the three different methods. The results show that CSPH and MSPH can both improve the numerical accuracy effectively, especially at the points near the boundary of a domain. In two dimensional cases, the accuracy of MSPH method is higher than that of CSPH method.
出处
《机械强度》
EI
CAS
CSCD
北大核心
2008年第1期78-82,共5页
Journal of Mechanical Strength
基金
国家自然科学基金(10577016)
国防基础科研(A2720060277)资助项目~~
