Numerical method for vorticity confinement in compressible flow

It is well known that modern computational fluid dynamics codes based on Eulerian descriptions do not adequately handle flows involving the convection of thin vortical layers. These layers often remain very thin and persist long distances without significant dissipation. Over the past decade, Steinhoff has introduced a class of methods, generally known as "vorticity confinement," which have been used successfully to predict complex flows, particularly involving helicopter rotors. These methods have involved an incompressible finite difference formulation. We extend vorticity confinement to compressible flows by noting that the confinement term added to the momentum equation in Steinhoff's formulation may be interpreted as a body force. We can then extend the approach to compressible flows by adding the contribution of this body force to the integral conservation laws. The development of a finite volume compressible vorticity confinement scheme then follows directly. We have implemented the scheme with a matrix artificial dissipation and a new matrix confinement term. Results are presented for supersonic shear layers, vortices moving in a uniform stream, and vortex separation on the leeward surface of a flat plate delta wing at supersonic speed.