大雷诺数Navier-Stokes方程的两水平亚格子模型稳定化方法

基于两重网格离散方法，提出三种求解大雷诺数定常Navier-Stokes方程的两水平亚格子模型稳定化有限元算法.其基本思想是首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程，然后在细网格上分别用三种不同的校正格式求解一个亚格子模型稳定化的线性问题，以校正粗网格解.通过适当的稳定化参数和粗细网格尺寸的选取，这些算法能取得最优渐近收敛阶的有限元解.最后，用数值模拟验证三种算法的有效性.

Two-level Subgrid Stabilized Methods for Navier-Stokes Equations at High Reynolds Numbers

Based on two-grid discretizations,three two-level subgrid stabilized finite element algorithms for stationary Navier-Stokes equations at high Reynolds numbers are proposed and compared. Basic idea of the algorithms is to solve a fully nonlinear Navier-Stokes problem with a subgrid stabilization term on a coarse grid,and then solve a subgrid stabilized linear fine grid problem based on one step of Newton,Oseen or Stokes iterations for Navier-Stokes equations.It shows that with suitable stabilization parameters and coarse and fine grid sizes,those algorithms yield an optimal convergence rate. Finally, numerial results are given to show efficiency of the algorithms.