N-S方程的非线性Galerkin算法的稳定性

On Stability of the Nonlinear Galerkin Methods for the Navier Stokes Equations

提出了求解二维非定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ（Ｎ－Ｓ）方程的３种全离散非线性Ｇａｌｅｒｋｉｎ算法，其中空间离散由谱元非线性Ｇａｌｅｒｋｉｎ算法进行，时间离散分别由Ｅｕ－ｌｅｒ法，修正的Ｇｒａｎｋ－Ｎｉｃｏｌｓｏｎ法和两步法进行．此外还分析了这些算法的有界性和稳定性。

This paper provides three kinds of fully discrete nonlinear Galerkin methods for solving the 2 D transient Navier Stokes equations. Spatial discretization is performed by the spectral nonlinear Galerkin method and time discretizations are made by Euler method,the modified Crank-Nicolson method and two step method. Moreover, the boundedness and stability of these methods are analyzed and the time step constraint conditions is provided.