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工程科学与技术:2010,42(1):91-97
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SPH离散误差的线性形式及稳定性分析
(哈尔滨工业大学 航天学院,黑龙江 哈尔滨150001)
Analysis on the Stability of SPH Based on the Linear Error Propagation of Spatial Discretizion
(School of Astronautics of Harbin Inst. of Technol., Harbin 150001,China)
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投稿时间:2008-10-15    修订日期:2009-07-19
中文摘要: 采用小量摄动法得到矩阵化后SPH算法的空间离散误差传播的线性形式及系统矩阵,并将其应用于SPH算法稳定性分析。分析该线性形式,得到与Swegle相同的张力不稳定性充分条件。忽略连续性方程的影响,分析系统矩阵的特征方程,可得到与系统矩阵的特征值存在等价特征值的2个矩阵,这2个矩阵可分别代表SPH的张力不稳定性和高频不稳定性。分析代表张力不稳定性的矩阵的性质,可知张力不稳定性是敏感于粒子间误差相位差异的;而分析代表高频不稳定性的矩阵,刚度矩阵秩缺陷导致高频不稳定性的进一步原因是粒子体积分布不均使得刚度矩阵对称性缺失。提出一个新的光滑长度更新模型,并使用于2个低雷诺数算例。
Abstract:The linear error propagation and its system matrix of the spatial discretization of matrix SPH, which was derived through perturbation method, were used to analyze the stability of SPH. Based on the linear form, the sufficient condition, which was ever obtained by Swegle, was also derived. Omitting the effect from the continuity equation and analyzing the characteristic equation of the system matrix, two matrixes, which having equivalent eigenvalues to those of the system matrix, were obtained and could respectively represent the existences of the tensile instability and the high frequency instability (HFI) in SPH. Based on the matrix that represents the existence of tensile instability, the tensile instability was found to be sensitive to the phase differences among the errors on particles. Based on other matrix that represents the existence of HFI of SPH, the origin of HFI, i.e. the rank deficiency in stiff matrix, was further found to be correlated with the asymmetry of the stiff matrix induced by the heterogeneous particle volumes. At last, another smoothing length refreshing model was proposed and was tested in two numerical cases.
文章编号:200800485     中图分类号:    文献标志码:
基金项目:国家自然科学基金
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郑俊,张嘉钟,于开平,魏英杰.SPH离散误差的线性形式及稳定性分析[J].工程科学与技术,2010,42(1):91-97.
Zheng Jun,Zhang Jiazhong,Yu Kaiping,Wei Yingjie.Analysis on the Stability of SPH Based on the Linear Error Propagation of Spatial Discretizion[J].Advanced Engineering Sciences,2010,42(1):91-97.