BUBBLE-STABILIZED SPECTRAL METHODS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

We present and investigate a stabilized spectral Legendre scheme for a pproximating the incompressible Navier-Stokes equations. The stabiliza tion is obtained by addinglocal bubble functions to the usual global p olynomial trial and testvelocities. This modification allows the use o f equal degree velocities and pressures; furthermore, in the advection -dominated regime, it induces an effectsimilar to the SUPG-effect in f inite elements. The method is validated on a Stokes flow and on the re gularized driven cavity flow at different Reynolds regimes; acompariso n with other spectral and finite element schemes is also provided.