Vorticity confinement application to flow around circular cylinders

Many flows which CFD is dealing with involve very thin vortical layers including boundary layers and shed vorticity. Conventionally, people have to use very fine grids and high order discretization to try to get the details of the internal structure of these thin vortical regions. Those methods may cost lots of computation time and still cannot give the right solutions. For example, in many of these flows the solutions near the surface can be determined by the details of the shed vorticity as much as by those of the internal structure of the boundary layer. A generalized Vorticity Confinement method, developed by John Steinhoff, represents the vortical layers as solitary wave solutions. This method involves adding a nonlinear negative diffusion term to the discretized momentum equations. Instead of the details of the internal structure, the integral effects of the thin region is computed, obeying the mass and momentum conservation laws. In addition to efficiently computing transport of shed vorticity, it allows the use of regular Cartesian coarse grids, which enables us to get reasonable solution without grid generation effort and with much less computation than other methods. The Vorticity Confinement method is applied to compute for flow around circular cylinders. This research is the first step towards the development of boundary layer models for blunt bodies in an incompressible flow. In this first step, only the "bare" scheme is used, without any "tunable" turbulence models.