A two-level finite element method for the Navier–Stokes equations based on a new projection ☆
A two-level finite element method for the Navier–Stokes equations based on a new projection ☆
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DOI：
10.1016/j.apm.2009.04.019
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发表时间：
2010-02
影响因子：
5
通讯作者：
Qingfang Liu;Yanren Hou
中科院分区：
文献类型：
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作者：
Qingfang Liu;Yanren Hou
基于含时投影，我们考虑了二维含时Navier-Stokes方程的全离散两级近似。通过定义这种新的投影，大小涡旋分量之间的迭代可以通过其相关的空间分裂来反映。因此，我们可以得到一个由大小涡流分量组成的弱耦合系统。该两层格式在空间上采用有限元方法，在时间上采用Crank-Nicolson格式。分析和数值算例表明，选择适当的粗网格尺寸h，两层格式可以达到与经典的一层Crank-Nicolson方法相同的精度，但所需的工作量要少得多。
We consider a fully discrete two-level approximation for the time-dependent Navier–Stokes equations in two dimension based on a time-dependent projection. By defining this new projection, the iteration between large and small eddy components can be reflected by its associated space splitting. Hence, we can get a weakly coupled system of large and small eddy components. This two-level method applies the finite element method in space and Crank–Nicolson scheme in time. Moreover,the analysis and some numerical examples are shown that the proposed two-level scheme can reach the same accuracy as the classical one-level Crank–Nicolson method with a very fine mesh size h by choosing a proper coarse mesh size H. However, the two-level method will involve much less work.