Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings,
Vol. 1, 1996, pp. 109-123
Computation of Incipient Separation Via Solution
of the Vorticity Equation on a Lagrangian Mesh
Stephen A. Huyer and John R. Grant
Naval Undersea Warfare Center
Hydrodynamics Branch
Newport, RI 02841, USA
Abstract
A novel vorticity based solution methodology has been developed to compute
unsteady flow, particularly separation. The vorticity of the flow is
determined on a set of points and the vorticity in the field 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 field. Triangulation of the vorticity field enables
computation of first and second order spatial derivatives of the vorticity
field using a least squares formulation. An effective diffusion transport
velocity was developed to account for spatial movement of the vorticity due
to viscosity. Diffusion velocity and direct calculation of the Laplacian
allows for a deterministic solution of viscous diffusion. The points are
then advected at both the induced velocity (computed from the Biot-Savart
integral) and the diffusion velocity. This solution scheme was found to be
stable as it was applied to the problem of impulsively started flow about a
NACA 0012 airfoil. The phenomena of incipient separation as well as
initial development of the unsteady wake was examined.
Vortex Flows and Related
Numerical Methods II
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