Navier-Stokes方程预处理方法及其对翼型绕流数值模拟的应用  

Development of an Efficient Viscous Preconditioning Method and Its Application to Numerical Simulation of Flows over Airfoils

作　　者：韩忠华[1] 乔志德[1] 熊俊涛[1] 何光洪[2] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国防科技重点实验室,陕西西安710072 [2]沈阳飞机设计研究所,辽宁沈阳110035

出　　处：《西北工业大学学报》2006年第3期275-280,共6页Journal of Northwestern Polytechnical University

基　　金：西北工业青年教师创新基金(M016204)资助

摘　　要：在与定常方程相容的情况下,通过对N av ier-Stokes方程的时间导数项实施Cho i及Turkel矩阵预处理,发展了适用于低、亚、跨声速粘性流动的有效的预处理方法。对预处理后的控制方程采用了Jam eson格式进行有限体积空间离散和Runge-K utta显示时间推进求解,以及采用了FA S多重网格方法加速收敛。对RAE 2822、GAW-1等不同类型翼型进行了低速和跨声速流动的数值模拟。算例表明:Cho i预处理方法和Turkel预处理方法均有效改善了时间推进方法对低马赫数流动计算的收敛性,而且提高了计算精度;预处理方法同样适用于跨声速非线性流动的计算,且表现出了一定的加速收敛效果。Purpose. Keeping in mind the perennial need for more and more efficient and robust computational codes used in numerical optimization design of airfoils, we investigate the preconditioning of NS （Navier-Stokes） equations. We introduce the preconditioning matrices proposed by Turkel and Choi into the time derivative terms of Reynolds-Averaged NS （RANS） equations. We remove effectively the system stiffness of compressible RANS equations for nearly incompressible flows and for flow region in the boundary layer of compressible flows. For the preconditioned RANS equations, we employ a cellcentered finite-volume scheme for spatial discretiztion and use a multi-stage Runge-Kutta method for time marching. A FAS （Full Approximation Scheme） multigrid method is also used to effectively accelerate the convergence to steady state. We simulated the low-speed, subsonic and transonic viscous flows over RAE2822 and GAW-1 airfoils respectively and achieved excellent success; the simulation results shown in Figs. 1 through 6 in the full paper （RAE2822 airfoil） and in Figs. 7 through 9 （GAW-1 airfoil） show good agreement with experimental data and exhibit rapid convergence. The comparison of the computed results and experimental data show that both Turkel＇s and Choi＇s preconditioning methods significantly improve the efficiency and accuracy of compressible computational code when used for low-speed flows. We also show that preconditioning method is applicable to accelerating the calculation of low-speed flow region in the boundary layer of subsonic and transonic airfoils. In short, we developed an efficient and robust code for low speed, subsonic, transonic and supersonic flows that can be used in numerical optimization design of airfoils.

关 键 词：Navier—Stokes方程 预处理方法 多重网格法 有限体积法 翼型 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]