An automatic anti-diffusion method for vortical flows based on Vorticity Confinement

Abstract

This paper describes an automatic Vorticity Confinement procedure in order to conserve vorticity in the resolution of the compressible Euler or Navier-Stokes equations. It is based on the cancellation of the leading truncation error terms in the numerical solution of the vorticity convection equation. Application to the simple case of the convection of a 2D vortex by considering the Euler equations shows that the procedure is adequate, although some problems lie at the vortex center, probably related to the compressible character of the equations and to the singularity associated to the confinement term at the vortex center. Further analysis suggests to consider the specific vorticity instead, thus imposing a corresponding density confinement term. The first results obtained so far indicate that this way of research is promising. However, it is shown that for fine grids, a regularization treatment must also be applied at the center of the vortex because of the Vorticity Confinement singularity. Finally, a first demonstration of the applicability of the method to 3D flows is given for the case of a vortex ring.