基于S-A湍流模型的Runge-Kutta有限元算法

A Runge-Kutta finite element algorithm based on the S-A turbulent model

采用一方程S-A模型(Spalart-Allmaras模型)封闭雷诺时均N-S方程(RANS方程)进行湍流数值计算,可以减少方程求解数量,节约计算时间。本文对其进行了有限元数值算法研究,首先通过沿流线坐标变换,得到无对流项RANS方程,并引入三阶Runge-Kutta法对其进行时间离散;然后利用沿流线的Taylor展开解决坐标变换带来的网格更新的困难;最后采用Galerkin法进行空间离散,得到湍流模型的有限元算法。基于方柱绕流和覆冰输电线绕流模型,与试验结果进行对比,验证了该算法的有效性,与一阶数值算法相比,该算法在精度和收敛性方面更具优势。

In the numerical calculation of turbulence, in order to reduce the number of solved equations and save computational cost, one-equation Spalart-Allmaras model is used to close Reynolds-averaged N-S equation.The research on turbulent numerical algorithm is carried out.Firstly, RANS equation without the convection term is obtained by coordinate transformation along streamlines, and the third-order Runge-Kutta method is introduced to discretize it in time.Then the Taylor expansion along streamlines is used to overcome the difficulty of mesh updating caused by the coordinate transformation.Finally, based on the Galerkin space discretization, the finite element algorithm of turbulence model is obtained.The numerical simulations of flow past a square cylinder and flow past an iced conductor are performed.Compared with the experimental results, the effectiveness of this algorithm is verified.Compared with the first-order algorithms, this algorithm has more advantages in accuracy and convergence.