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A characteristic-based four order Runge-Kutta finite element method for incompressible viscous flow[J].计算力学学报,2019,36(2):226~232

A characteristic-based four order Runge-Kutta finite element method for incompressible viscous flow
A characteristic-based four order Runge-Kutta finite element method for incompressible viscous flow

DOI：10.7511/jslx20171201001

 作者 单位 E-mail 廖绍凯 嘉兴学院 建筑工程学院, 嘉兴 314001河海大学 力学与材料学院, 南京 211100 张研 河海大学 力学与材料学院, 南京 211100 yan.zhang@hhu.edu.cn 陈达 河海大学港口海岸与近海工程学院, 南京 211100

对于二维不可压缩粘性流，通过沿流线方向的坐标变换，推导了无对流项的二维N-S（Navier-Stokes）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，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。

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 fourth 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,a high precision finite element algorithm is obtained.This algorithm is applied to simulate flow in a cavity and flow around a circular cylinder.Through analyzing the effects of the different time step sizes,mesh sizes and flow field regions,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.