A general approach to vorticity confinement development for high-order flow solvers

The vorticity confinement technique is analyzed for a family of flow solvers based on upwind-biased differentiation schemes. Treating the necessary confinement level as a numerical error leads to a new technique for developing advanced confinement terms when the basic formulation is unable to preserve the vortex properties. It is show that for third- and fifth-order upwind-biased solvers, the error in vortex convection is substantially different than what is seen in a simple first-order scheme, explaining the original difficulty in developing a confinement term that is independent of grid density, vortex strength, and convection Mach number for these schemes. A functional confinement term is shown for the first-order scheme, and the difficulties in developing high-quality parameters for the higher-order schemes are discussed.