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力学与实践 ›› 2010, Vol. 32 ›› Issue (3): 16-21.doi: 10.6052/1000-0879-2009-344

• 应用研究 • 上一篇    下一篇

计算含动边界非定常流动的无网格算法

周星 许厚谦   

  1. 南京理工大学动力学院804教研室
  • 收稿日期:2009-09-03 修回日期:2009-11-18 出版日期:2010-06-08 发布日期:2010-06-08

THE MESHLESS METHOD FOR UNSTEADY FLOW WITH MOVING BOUNDARY

ZHOU Xing XU Houqian   

  • Received:2009-09-03 Revised:2009-11-18 Online:2010-06-08 Published:2010-06-08

摘要: 在无网格算法中考虑了含动边界的流动问题,研究了可以计算处理包含一定位移及扭转动边 界非定常流动的算法. 创建了无网格算法的动点法则,并引入抗扭方法对弹簧方法进行改进 来处理离散点运动,提高了方法的可用度及精度. 发展了求解基于无网格的ALE方程组的算法, 在点云离散的基础上采用曲面逼近计算空间导数及HLLC格式计算数值通量,运用四步龙格- 库塔法进行时间推进. 在跨、超音速条件下,计算模拟了典型翼型简谐振动流场,计算结果 与实验结果及文献对比吻合,验证了该算法的正确性.

关键词: 无网格;弹簧方法;ALE方程;颤振;数值模拟

Abstract: The meshless method is used to solve problems with moving boundaries, A method is proposed for dealing with unsteady flow with movable and torsional boundaries in small scale. The moving principle for discrete points in meshless method is formulated, the spring analogy is modified to consider the movements of points, the adaptability and precision of the analogy are enhanced. ALE equations are solved based on meshless method. Based on clouds, the spatial derivatives are approximated by using local least-squares curve fitting and the numerical flux is calculated with HLLC scheme, a multistage Runge-Kutta algorithm is used to advance the equation in time. The oscillating flow of representative airfoils in transonic and supersonic conditions is simulated. The computational results agree well with the experiment data, which indicates that the method is valid.

Key words: meshless method, spring analogy, ALE equations, oscillation, numerical simulation