非定常Navier-Stokes 方程基于H（div）型有限元的涡旋黏性法

Eddy viscosity method by H(div) elements for the time-dependent Navier-Stokes equations

摘要:

本文将子格涡旋黏性思想与H（div）型有限元逼近（比如RT元和BDM元）相结合, 对不可压非定常Navier-Stokes方程提出了一种新的稳定化有限元格式. 这种格式不仅满足守恒条件, 而且克服了对流占优所引起的震荡. 然后通过半离散有限元格式, 得到了与约化雷诺数相关与雷诺数无关的误差估计.

Abstract:

In this paper, the authors propose a new stabilized finite element formulation for the incompressible time-dependent Navier-Stokes equations with high Reynolds number. This formulation combines subgrid eddy viscosity methods with H(div) finite element approximation, for example RT and BDM finite element. This method not only satisfies the conservation condition but also controls spurious oscillations in the velocities due to the convection dominated. We derive the stability and error estimates for finite element semidiscrete scheme which combines subgrid scale eddy viscosity method with \textbf{H}(div) elements. In addition, the constants in these error estimates do not depend on the Reynolds number but on a reduced Reynolds number.