Vortex Methods with Spatially Varying Cores

The accuracy of vortex methods employing smooth vortex particles/blobs is determined by the blob size, which can be viewed as a mollifier of the vorticity field. For computational efficiency, this core size needs to be spatially variable as particles are used to discretize different parts of the flow field, such as the boundary layer and the wake in bluff body flows. We derive here a consistent approximation for the viscous Navier–Stokes equations using variable size vortex particles. This derivation is based on the implementation of mappings that allow the consistent formulation of the diffusion and convection operators of the Navier–Stokes equations in the context of vortex methods. Several local mappings can be combined giving the capability of “mesh-embedding” to vortex methods. It is shown that the proposed variable method offers a significant improvement on the computational efficiency of constant core size methods while maintaining the adaptive character of the method. The method is ideally suited to flows such as wakes and shear layers and the validity of the approach is illustrated by showing results from cylinder flows and wall-vortex interactions. Using this scheme, previously unattainable simulations of cylinders undergoing rotary oscillations at high Reynolds numbers reveal an interesting mechanism for drastic drag reduction.