本文讨论在非正交曲线坐标系中 ,粘性流矢量方程一种新的展开思路。应用这种展开方法可以得到项数减少很多的展开式 ,便于工程计算。文中同时给出了可压缩与不可压缩方程的展开式 ,给出了统一方程表达式。最后对二维不可压叶栅粘性流和三维可压叶栅粘性流进行了数值计算 ,计算表明本文给出的新展开方程是有实用价值的 In this paper, we discuss a new concept of viscous flow vector equation in non-orthogonal curvilinear coordinate system. Application of this method can be expanded to get a lot less number of expansion, easy to engineering calculations. In the meantime, the expansion of compressible and incompressible equations is given, and the expression of uniform equation is given. Finally, two-dimensional incompressible cascade viscous flow and three-dimensional compressible cascade viscous flow are numerically calculated. The calculation shows that the new expansion equation given in this paper is of practical value