扩散抛物化(DP)NS方程组的意义及其在计算流体力学中的应用

Significance of diffusion-parabolized NS equations and its application to computational fluid dynamics

本文首先讨论扩散抛物化(DP)NS方程组的早期研究工作:它的提出、数学性质、意义和在CFD中的应用,然后讨论扩散抛物化理论的一些新发展。这些新发展是对NS方程组数值计算进行物理分析的基础上得到的,其中包括NS方程组差分计算时,粘性剪切流对网格间距和格式精度的要求;粘性项只保留剪切粘性项的广义扩散抛物化(GDP)NS方程组,它的性质和应用。由于高Re数流动在NS方程组的差分计算中,网格Re数彼此相差悬殊的特点,产生了计算离散单元守恒方程组的新的算法思路,即离散流体力学(DFD)算法。在DFD算法中需要同时计算三种不同的守恒方程组(Euler,DPNS和NS方程组)。本文讨论了DFD格式的构造、它的优点和应用。并以超声速绕前后台阶流动为算例,来说明GDPNS方程组的用处和DFD算法的优点。DPNS方程组、GDPNS方程组、DFD算法是高智提出的,对这些问题,他和合作者从理论、算法、数值验证和某些应用又作了系统的研究。

Early research works of diffusionparabolized NS equations were firstly discuss ed: its proposal, mathematic characteristics, significance and application to Co mputational Fluid Dynamics. Meanwhile, the new developments of diffusionparabo lized NS equations have been reviewed, which were obtained by physical analyses on the numerical results of NS equations. Since the difference of grid Re nu mber in numerical calculation of high Re number flow was very large, a new c omputational method called the DFD method was produced. In DFD method three diff erent conservation equations, Euler equations, DPNS equations and NS equations, have been adopted simultaneously. In this paper the construction and advantages of DFD scheme as well as its application are discussed. The advantages of GDPNS equations and DFD method are shown by three numerical examples. DPNS equations, GDPNS equations and DFD method were first presented by Gao Zhi. He and his stude nts have verified numerically the correctness and effectiveness of these equatio ns and methods. Key words: computational fluid dynamics; diffusion parabolized NS equations; discrete fluid dynamics methodSubsonic and transonic wing inverse design using control theoryYANG Xudong, QIAO Zhide, ZHU Bing(Northwestern Polytecnical University Xi'an 710072, China) Abstract: Based on control theory, the wing inverse design problem is studied in present p aper. A numerical method has been developed for solving the three dimensional ad joint equations corresponding to Euler equations in physical space, and some mea sures have been taken, such as far field conditions using characteristics theory , accelerating the convergence of the costate variables through the addition o f carefully controlled numerical diffusive terms. By using HicksHenne function , wing surface variation caused by perturbation of design variables is taken int o account. The gradient of objective function for design variables can be obtain ed by using grid perturbation method,a quasiNewton algorithms is used. Some n umerical tests have been made for the inverse design. The test results show that the present method is effective and feasible in the case of both subsonic and t ransonic wing inverse design, and the computational time is acceptable by CFD re searcher. 