| 瞬态问题稳定性及弥散分析的无网格RKPM配点法研究 |
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| 引用本文： | 罗汉中,刘学文,黄醒春.瞬态问题稳定性及弥散分析的无网格RKPM配点法研究[J].应用数学和力学,2011,32(6):730-740. |
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| 作者姓名： | 罗汉中 刘学文 黄醒春 |
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| 作者单位： | 上海交通大学 船舶海洋与建筑工程学院,上海 200240; |
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| 基金项目： | 交通部西部交通建设科技资助项目(2009318000046) |
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| 摘 要： | 介绍了基于强形式的RKPM配点法求解瞬态动力问题的算法，并提出了采用RKPM配点法，配合时间域中心差分求解二阶波动方程的稳定性评价方法，并通过数值算例验证了此方法的正确性．此评价方法可以方便有效地评估出实际计算时的临界时间步长．通过数值算例比较可知，实际算例的计算临界时间步长与本评价方法，所预测的临界时间步长结果非常接近．给出了如何合理地选择RKPM形函数支撑域的建议．最后与径向基函数配点法进行了对比研究．
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| 关 键 词： | RKPM配点法 稳定性分析 弥散分析 瞬态动力问题 |
| 收稿时间： | 2010-07-21 |
Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics |
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| LUO Han-zhong,LIU Xue-wen,HUANG Xing-chun.Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics[J].Applied Mathematics and Mechanics,2011,32(6):730-740. |
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| Authors: | LUO Han-zhong LIU Xue-wen HUANG Xing-chun |
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| Institution: | School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, P. R. China;Siemens Industry Software(China) Co., Ltd., Shanghai 200042, P. R. China |
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| Abstract: | Reproducing kernel collocation method based on strong formulation was introduced for transient dynamics.von Neumann stability and dispersion analysis of reproducing kernel collocation method with central difference temporal discretization was derived to evaluate the stability condition for second order wave problem.The stability analysis algorithm proposed firstly given an approach to predict critical time step for second order wave problem which can greatly save computational time in application.A numerica... |
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| Keywords: | reproducing kernel collocation method(RKCM) stability analysis dispersion analysis transient dynamics |
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