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

摘要

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