Navier-Stokes方程的最佳有限元非线性Galerkin算法

1．引言对于Navier－Stokes方程有限元数值求解方面的研究已有很多的文章和专著，多数是采用有限元Galerkin算法，例见文献[1-4]．然而，由于Navier-Stokes方程在大雷诺数时有其强的非线性性和对时间土的长期依赖性，用计算机求解Navier－Stokes方程在速度和容量方面是难以承受的．为了克服这些困难，最近人们提出了有限元非线性Galerkin算法，见文献卜8］，然而这种算法只是在某一有限时刻之后具有好的收敛速度，在初始时刻的某一区间不能达到好的收敛速度．本文应用Taylor展开技术导出了数值求解二维非定常Navier－Stokes方程的最佳…

OPTIMUM FINITE ELEMENT NONLINEAR GALERKIN ALGORITHM FOR THE NAVIER-STOKES EQUATIONS

A optimum ffote element nonlinear Galerkin algorithm is presented for thetwo-dimensional nonstationary Navier-Stokes equations. The standard finite elemellt Galerkin algorithIn consists in solving a nonlinear equation on the fine gridfinite elemellt space Xh' The optimum finite element nonlinear Galerkin algorithm consists in solving a nonlinear subproblem on a coarse grid finite elementspace XH(H > h) and solving a linear subproblem on a fine grid incremental finite element space Wh = (I - RH)Xh- If H is chosen such that H = O(h1/2),then two algorithms are of the c0nvergence rate of same order. However, sinceH >> h, dimXH << dimXh, the optimum finite elemellt nonlinear Galerkin algorithm can save a large amoullt of comPutational time. Finally, we give thenumerical test which shows the correctness of theoretical analysis.