Development of artificial dissipation schemes and compressible vorticity confinement methods

Abstract

The conventional vorticity confinement methods have a constant confinement parameter that should be determined for every problem by trial and error. In this article, vorticity confinement parameters are successfully developed for compressible flows. The first new confinement parameter is proportional to spectral radii of the flux Jacobian matrix. Therefore, the confinement parameter implicitly contains the grid size and the other local fluid properties. In order to gain confidence in the applicability of vorticity confinement, it would be ideal to completely eliminate such constant parameters. In the next part of this article, a suitable relation is introduced for the vorticity confinement parameter that does not need any constant coefficient. The scalar dissipation scheme (SCDS-1) and matrix dissipation scheme (MADS-1) are two common artificial dissipation schemes that have been used for several years. Two new artificial dissipation schemes are introduced by using the QUICK scheme in this article (SCDS-2, MADS-2). The capabilities of these four artificial dissipation schemes are compared for channel flow problem. Then, the new confinement parameters and artificial dissipation schemes are used for solving moving vortex in a uniform flow and supersonic shear layer problems. The methods have been shown to be very effective at treating shock waves and vortex dominant flows.