Computation of Incipient Separation via Solution of the Vorticity Equation on a Lagrangian Mesh

A novel vorticity based solution methodology has been developed to compute unsteady ow, particularly separation. The vorticity of the ow is determined on a set of points and the vorticity in the eld is computed by linear interpolation. This is accomplished by the construction of a connected set of triangular elements formed by Delaunay triangularization of the points in the eld. Triangulation of the vorticity eld enables computation of rst and second order spatial derivatives of the vorticity eld using a least squares formulation. An eeective diiusion transport velocity was developed to account for spatial movement of the vorticity due to viscosity. Diiusion velocity and direct calculation of the Laplacian allows for a deterministic solution of viscous diiusion. The points are then advected at both the induced velocity (computed from the Biot-Savart integral) and the diiusion velocity. This solution scheme was found to be stable as it was applied to the problem of impulsively started ow about a NACA 0012 airfoil. The phenomena of incipient separation as well as initial development of the unsteady wake was examined.