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粘性流基于特征线的四阶Runge-Kutta有限元法
A characteristic-based four order Runge-Kutta finite element method for incompressible viscous flow
投稿时间:2017-12-01  修订日期:2018-01-24
DOI:
中文关键词:  Navier-Stokes方程  四阶  Runge-Kutta法  收敛性  耗散性  精度
英文关键词:Navier-Stokes equation  four order  Runge-Kutta method  convergence  dissipation  accuracy
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
作者单位E-mail
廖绍凯 嘉兴学院 liaoshaokai@163.com 
张研 河海大学  
陈达 河海大学  
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中文摘要:
      对于二维不可压缩粘性流,本文通过沿流线方向的坐标变换,推导了无对流项的二维Navier-Stokes(N-S)方程。采用四阶Runge-Kutta法对N-S方程进行时间离散,并沿流线进行Taylor展开得到显式的时间离散格式,然后利用Galerkin法对其进行空间离散,进而得到了高精度的有限元算法。利用本文算法对方腔驱动流和圆柱绕流进行了数值计算,通过对不同大小的时间步长,网格尺寸和流场区域的计算分析,进一步验证了本文算法相比经典CBS法在时间步长,收敛性,耗散性和计算精度方面更具有优势。
英文摘要:
      For two-dimensional incompressible viscous flow, the two-dimensional Navier-Stokes (N-S) equation without convection term is derived by the coordinate transformation along the streamline direction. the explicit time discrete format is obtained via introducing the four order Runge-Kutta method and the Taylor expansion along the streamline direction, and then the space discretization format is carried out by the Galerkin method, finally, the high precision finite element algorithm is obtained. This algorithm is applied to simulate flow in a cavity and flow past a circle cylinder. Through analyzing the effects of the different time step size, mesh size and flow field region, the algorithm is further validated. Compared with the classical CBS method, it has more advantages in time step, characteristics of convergence and dissipation and accuracy.
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