非定常Navier-Stokes方程的一种非线性局部投影稳定化有限元方法

A nonlinear local projection-based finite element method for unsteady Navier-Stokes equations

摘要:

针对非定常Navier-Stokes方程, 本文提出了一种基于非线性对流项和压力梯度的局部投影稳定化有限元方法. 该方法在空间上采用等阶有限元, 时间上采用隐式有限差分. 本文建立了非定常Navier-Stokes方程的全离散数值格式, 进而分析了离散解的稳定性和收敛性. 值得注意的是，该方法中得到的误差估计随着流体雷诺数的增大依然有效.

Abstract:

In this study, a stable local projection finite element method is derived for unsteady Navier-Stokes equations. This method is formed by local projection of advection term and pressure gradient. By using the equal-order conforming finite elements in space and implicit finite difference scheme in time, we derive a full discrete formulation and prove the stability and convergence of the approximation solution. Notably, the error estimates hold even for large Reynolds numbers.