间断Galerkin算法求解三维RANS方程  

Discontinuous Galerkin method for 3-D RANS equations

作　　者：奉凡[1] 顾春伟[1] 李雪松[1] 

机构地区：[1]清华大学热能工程系,热科学与动力工程教育部重点实验室,北京100084

出　　处：《清华大学学报（自然科学版）》2010年第11期1834-1837,1842,共5页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(50776051);国家“九七三”重点基础研究项目(2007CB210105)

摘　　要：研究了间断Galerkin(DG)算法在三维可压缩湍流流场模拟中的应用。采用DG算法求解RANS方程和SA湍流模型方程,使用Roe格式计算无粘通量。针对RANS方程中的粘性项,发展了一种适用于DG算法的高效的高阶精度梯度计算方法。该方法以计算坐标系下守恒变量的梯度作为混合有限元法的辅助未知量,可使梯度计算达到与守恒变量相同阶的精度,并且不需要计算数值积分。采用该文描述的算法计算了NACA 64叶栅的三维湍流流场,得到了与实验数据吻合良好的结果,表明DG算法在叶轮机械内部湍流流场计算方面具有广阔的应用前景。The application of discontinuous Galerkin method（DGM） was investigated to simulate 3-D compressible turbulence flow field.DGM was used to solve the Reynolds-averaged Navier-Stokes equations closed by S-A turbulence model.Roe scheme was adopted as numerical flux of inviscid terms at the element interface.An efficient algorithm was developed to evaluate the gradients in the viscous terms for high-order accurate DGM.In the algorithm the gradient of conservative variables in the computational space is treated as auxiliary unknowns of mixed formulation,which were solved to the same order of accuracy as the conservative variables without need of quadrature.The 3-D turbulence flow field in compressor cascade NACA64 was simulated and numerical results agree well with the experimental data,which demonstrates the accuracy and capability of DGM in the simulation of turbulence flow in turbomachinery.

关 键 词：间断Galerkin算法 湍流模拟 SA模型 

分 类 号：O354[理学—流体力学]