用惩罚拟协调元法分析二维N-S问题

Analysis and Calculation of 2-D Naveir-Stokes Problem by Penalty-Quasi Conforming Technique

给出构造 Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ问题罚有限单元的拟协调元法。在处理剂次约来离散 矩阵的奇异性问题时，暂代减缩积分，利用多套函数的灵活性和秩的分析方法，进行 秩的预先设计，成功地构造出－１２参三角形拟协调单元。以求解正方形空穴流动为 例，在网格的粗的情况下，求得了雷诺数为３ ０００的稳定、收敛的解。在求解离散 化的非线性方程组时，将最优化法与增量－牛顿法结合使用，改善了迭代格式的适应 性能，提高了计算效率。公式推导过程和试验结果表明分忻与求解方法是有效的。

The Quasi-Conforming Element(QCE) technique is introduced of constructing penalty finite element of Navier-Stokes Problem.Unlike the Reduced Integration methods, the QCE technique designates the rank a prior to ensure that matrix which represents the discretization of the homgeneous constrain is singular or rank deficiency by its adaptability of multiple sets of functions and is indepen- dent of the integration order. A 6-node triangle Penalty-Quasi Conforming Element is used for analyzing and calculating the square driven cavity problem and a stable and coverged result is obtained when its Reynods number amounts to 3000.