中文摘要：

运用张量分析理论，分别给出了标量、矢量以及二阶张量等任意阶数张量的Gauss定理，并应用到积分形式流动控制方程的推导中，得到具有普遍意义的三维任意曲线坐标系上的积分守恒型N—S方程的通用形式，并采用有限体积的时间推进法对方程进行数值离散，研制了相应的CFD分析程序．作为算例，对具有复杂边界的大尺度离心叶轮内的旋转三维湍流场进行了数值模拟．与实验结果的比较表明，数值模型和解法是成功的，为复杂物理域的流动问题的数值模拟奠定了基础．

英文摘要：

Gauss theorem for tensor of any order, such as scalar, vector and second order tensor, is presented with a tensor analysis technique. A general integral conservation form of Navier-Stokes equations in any three-dimensional curvilinear coordinate is derived. A timemarching algorithm coupled with finite volume is applied to discretization of the governing equations. A CFD code is developed to simulate a three dimensional rotating viscous flow field inside an NASA low-speed centrifugal compressor （LSCC） impeller with vaneless diffuser. Numerical algorithm and general integral conservation form of N-S equations are validated with experimental data. It provides a study basis for complex physical region.