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

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.