Development and Application of Compressible Vorticity Confinement

In this paper, variable confinement parameters were successfully developed for compressible vorticity confinement. Three variable confinement parameters, that have velocity dimension, were defined, based on three artificial dissipation schemes. The resulting confinement parameters are functions of the spectral radii of the Jacobian matrices and the Jacobian matrices themselves. Therefore, the confinement parameter implicitly contains the grid size and other local fluid properties. Preliminary results for moving vortices showed that the new confinement parameters allow the capture of vortical layers that, effectively, do not decay in time, like Hu et al.'s confinement. Calculations of the supersonic base flow and supersonic shear layer showed good agreement with experimental and analytical data, especially for the variable CUSP confinement parameter. When variable confinement parameters are used, the tuning constant is equal to, or larger than, the equivalent value of the constant confinement (Hu et al.). This means that the tuning constant varies in a range smaller than that of the Hu et al. constant confinement, especially for the CUSP confinement parameter.