| SPH离散误差的线性形式及稳定性分析 |
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| 引用本文： | 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].四川大学学报(工程科学版),2010,42(1):91-97. |
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| 作者姓名： | 郑俊 张嘉钟 于开平 魏英杰 |
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| 作者单位： | 哈尔滨工业大学航天学院,黑龙江哈尔滨,150001 |
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| 基金项目： | 国家自然科学基金资助项目(10832007) |
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| 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,并使用于两个低雷诺数算例.
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| 关 键 词： | SPH算法 空间离散误差 系统矩阵 张力不稳定性 高频不稳定性 |
| 收稿时间： | 2008/10/15 0:00:00 |
| 修稿时间： | 2009/7/19 0:00:00 |
Analysis on the Stability of SPH Based on the Linear Error Propagation of Spatial Discretizion |
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| Zheng Jun,Zhang Jiazhong,Yu Kaiping and Wei Yingjie.Analysis on the Stability of SPH Based on the Linear Error Propagation of Spatial Discretizion[J].Journal of Sichuan University (Engineering Science Edition),2010,42(1):91-97. |
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| Authors: | Zheng Jun Zhang Jiazhong Yu Kaiping and Wei Yingjie |
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| Affiliation: | ZHENG Jun,ZHANG Jia-zhong,YU Kai-ping,WEI Ying-jie(School of Astronautics of Harbin Inst.of Technol.,Harbin 150001,China) |
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| 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 ... |
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| Keywords: | SPH space discretization error system matrix tensile instability high frequency instability |
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