不可压N-S方程的高阶计算方法  

High Order Scheme for Incompressible Navier-Stokes(N-S) Equations with Application to MAV(Micro Air Vehicle)

作　　者：谢飞[1] 叶正寅[1] 

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

出　　处：《西北工业大学学报》2007年第3期368-373,共6页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(10372085)资助

摘　　要：采用拟压缩方法求解了不可压缩N-S方程,时间推进上采用隐式的LU-SGS方法,空间上采用R oger的五阶迎风格式。以圆柱和低雷诺数翼型绕流为计算对象,研究了这种高精度格式在低雷诺数问题中的适应性,同时分析了不同的空间精度、人工粘性等对结果的影响。结果表明:对于圆柱绕流而言,中心格式下面较大的人工粘性会延迟漩涡的周期性脱离;空间精度越高,对分离涡的刻画越细致,漩涡的周期性脱离开始得越早。Aim. One reason why existing schemes for the incompressible N-S equations are not satisfactory is, in our opinion, that their order is low. We now present a scheme that is relatively high in order. In the full paper, we explain our scheme in detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is： the calculation. In the first topic, we mention that： （1） the incompressible N-S equations are solved with the method of pseudo-compressibility, and the implicit LU-SGS method is used for time stepping; （2） the fifth-order upwind differencing method developed by Roger is employed. The second topic is： the verification of our fifth-order scheme with three instances. The three subtopics of the second topic are： the simulation of the flow field around a cylinder using Re=200 （subtopic 2. 1）, the simulation with Re=105 （subtopic 2. 2）, and the simulation of the flow field around E387 airfoil using Re=100 000 （subtopic 2. 3）. In subtopics 2. 1, we present the simulation results, as shown in 4 figures in the full paper： （1） the differencing method is reliable; （2） the centered scheme with more artificial dissipation delays the periodic shedding of the vortex in the flow field around the cylinder; （3） the higher-order scheme can describe the shedding vortex more accurately, and the shedding begins earlier. In subtopic 2.2, we present a rather fine vorticity field as shown in Fig. 6 in the full paper. In subtopic 2.3, our simulation results show preliminarily that. （1） in the case of low Reynold number, even a small angle of attack can make the airflow around the airfoil separate; （2） the separation on the surface of E387 airfoil causes the increase of its lift coefficient.

关 键 词：拟压缩 五阶迎风 隐式LU-SGS 

分 类 号：V211[航空宇航科学与技术—航空宇航推进理论与工程]