瞬态问题稳定性及弥散分析的无网格RKPM配点法研究  

Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics

作　　者：罗汉中[1] 刘学文 黄醒春[1] 

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200240 [2]西门子工业软件(上海)有限公司,上海200042

出　　处：《应用数学和力学》2011年第6期730-740,共11页Applied Mathematics and Mechanics

基　　金：交通部西部交通建设科技资助项目(2009318000046)

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.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 numerical test was conducted to validate this algorithm. The comparison of numerical critical time step and predicted results shows good agreement. The guidance to choose a proper support size of reproducing kernel shape function is also given. The results by radial basis collocation method are also listed for comparison.

关 键 词：RKPM配点法 稳定性分析 弥散分析 瞬态动力问题 

分 类 号：O302[理学—力学]