关于三维Navier－Stokes方程的粘性项计算

On Numerical Computation of Viscous Terms for 3-D Navier-Stokes Equations

借助于张量分析和张量计算，在贴体曲线坐标系下本文讨论了不同求解变量导致了粘性项个数上的重大差异和不同大小的计算量，并提出了便于粘性计算的最佳形式。文中借助于有限体积离散技术，通过引进两个对称辅助矩阵［Ａ］和［Ｂ］，使粘性项的计算量大大减少，这对完成三维粘性流的数值计算具有重要的指导意义。借助于上述方法，本文完成了某型真实进气道两种工况的三维粘性Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程计算（即Ｍ∞＝３．０，α＝０°和设计工况Ｍ∞＝２．６５，α＝０°），获得了满意的全场结果；对于Ｍ∞＝２．６５的设计工况，同实验数据作了比较，符合良好。由于本文的方法明显的减少了粘性项的计算量且节省了大量内存，以致于使三维流场的Ｎ－Ｓ求解能在普通微机上进行。

Differen tforms for viscous terms of three-dimensional Navier-Stokes equations with different primeval variables are discussed by usingtensor analysis technique in curvilinear coordinate system and two effec-tive approaches for computation of viscous terms are presented in thispaper.These are:(1) an optimum form of Navier-Stokes equations forfinite-difference method is given.(2)the auxiliary matrixes[A]and[B]are considered by using finite-volume technique. They provide efficientmethods for calculating three-dimensional compressible viscous flows. Themethods were used to compute the external and internal flow field foran inlet. Results were obtained for two flow conditions(M_∞=3.0 andα=0°,M_∞=2.65 and α=0°).Some of the computed results were comparedwith wind tunnel data. The computations and experimental results com-pare reasonably well. Numerical application shows that the present me-thod needs less computer storage and CPU time.