中文摘要：

目前所有的计算方法（如有限元方法、有限容积法或无网格方法）在计算时均需要较长的计算时间,很难直接应用于工业中的实时控制。该文应用最佳正交分解（proper orthogonal decomposition,POD）方法从不可压缩流动问题的流场中抽取特征函数,并用Galerkin方法将特征函数对N-S方程进行投影,得到N-S方程的降阶模型。通过一个具有分析解的例子验证该方法的精度与有效性。计算结果表明：POD方法计算得到的特征值的大小反应了它所能捕捉到流场中的广义＂能＂大小,最大特征值所对应的特征函数能很好地捕捉到流场的特征;降阶模型的计算结果与有限容积法的计算结果符合得很好,但能节省更多的计算时间,因此降阶模型能直接应用于工业中的实时控制。

英文摘要：

The conventional numerical methods（such as finite element method（FEM）,finite volume method（FVM） and meshless method） cannot be directly applied in a real-time processing control because they need more time-consuming.The proper orthogonal decomposition（POD） method was applied to extract eigenfunctions from incompressible fluid flow problem,and reduced order method（ROM） can be obtained by projecting the eigenfunction to Navier-Stokes equation using Galerkin method.A case that has analytical solution was applied to validate efficiency and accuracy of the present method.The computational results show that the eigenvalues can be obtained by the POD method and the magnitude of eigenvalues denote that they can capture the magnitude of the ＂energy＂ of flow field,the eigenfunction corresponding to the maximum eigenvalue can capture the characteristic of flow field well enough.The computational results of ROM are in very good agreement with that of FVM,but ROM can save more computational time.Thus,such ROM can be directly applied to the real-time processing control of industry.