基于旋转坐标系的高阶间断有限元方法非定常湍流数值模拟

基于高阶间断有限元方法(Discontinuous Galerkin method,DGM),对旋转非惯性系下耦合了修正的一方程S-A模型的RANS方程进行了离散求解。为了在稀疏网格上获得更贴近真实的物面形状,使用了多层高阶弯曲网格方法对物面进行拟合。非定常时间推进采用了隐式双时间步方法,每个时间步产生的线性系统采用预处理的方法,即广义最小残差方法(Generalized minimal residual method,GMRES)来求解。计算了旋转圆柱绕流以及经典翼型振荡算例的升力和力矩迟滞曲线,与实验结果以及前人的计算结果对比验证了本文方法的正确性和有效性。

Numerical Simulations of Turbulent Flow Based on Rotating Reference Frame Using High-Order Discontinuous Galerkin Method

The RANS equations coupled with modified S-A model in a rotating reference frame are solved using the high-order discontinuous Galerkin method (DGM). In order to obtain more accurate wall boundaries on relatively coarse grids, a multilevel high-order curved mesh method is employed. An implicit dual time stepping method is adopted for the unsteady simulation, while generalized minimal residual method (GMRES) is deployed to solve the large linear system generated in each time step. The lift and moment hysteresis curves of rotating cylinder flow and classical airfoil oscillation are calculated. The correctness and validity of the proposed method are verified by comparing with the experimental results and previous calculation results.