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中文摘要：
在这篇文章中，运用经典的张量分析方法，把流动区域用一个二维流形序列分割成一系列流层之并，推得在流层内半测地坐标之下的Navier—Stokes方程，在流形的法线方向应用向后Euler差分，推导了两维流形上的可压缩Navier—Stokes方程，和流函数满足的方程．在这个基础上，提出了一种维数分裂法的新算法．这种方法不同于区域分解法．对于三维问题，在区域分解法中我们必须在每个子区域上仍解三维问题，但是在这种新方法中，只需要在每个子区域上求解二维问题，不过是几个二维流形上的NS方程．文中还给出了一个透平机械内部流动的数值计算实例．
英文摘要：
In this paper, 3D-flow domain is decomposed into a series of thin stream flow layers by a series of 2D-manifolds（surface） using calssical tensor anslysis method. Applied Euler backward difference scheme along normal direction to manifold, the compressible Navier-Stokes equations on the 2D-manifold are derived. Accoding to this idea, a dimension split method is proposed.this method is different from the classical domain decomposition method, in which one must solve a 3D problem into each subdomain, but in our method we only solve a 2D-subproblem on 2D manifold, which is a quasi-Navier-Stokes equations on 2D manifold. In addition, the paper provide several numerical examples for turbomachinary flow.
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