離散渦漩法之進階研究(II)

Some time ago, the present authors proposed a
hybrid vortex method for study of two-dimensional
separated flows. It is hybrid in that a grid is required,
and therefore is not fully Lagrangian. It is also
deterministic that no random walk for diffusion is
employed. The method is here extended to threedimensional
separated flows. Such an extension is not
at all obvious but requires new definition and
formulation of the previous method. The method
may be briefly described as follows. At any instant, a
collection of vortices forms a patch of the flow field.
The methods consists of solving the viscous vorticity
equation by evolving a total vorticity associated with
each vortex, and then redistributing the evolved total
vorticity back to the grid at the end of each time step.
The total vorticity, when divided by the volume that it
occupied, yields the mean vorticity associated with the
vortex. The velocity field is recovered from the
vorticity field by solving a Poisson equation for a
vector stream fucntion. It is shown consistent to
specify the gauge that a component of the vector
stream function be identically zero; this facilitates
imposing Dirichlet conditions for the other two
components on the body surface to satisfy the nonpenetrating
condition. Vorticity is then updated on the
body surface to fulfill the no-slip condition. The
overall method here presented is a quite general setting
for a finite body but with a particular application to
flow about an impulsively started sphere. Preliminary
results shows excellent comparisons with measured
data in several detailed flow chatracteristics.