  The present paper suggests a method for obtaining incompressible solenoidal
velocity vectors that satisfy approximately the desired immersed velocity
boundary conditions. The method employs merely the mutual kinematic relations
between the velocity and vorticity fields (i.e, the curl and Laplacian
operators). An initial non-solenoidal velocity field is extended to a regular
domain via a zero-velocity margin, where an extended vorticity is found.
Re-calculation of the velocities (subjected to appropriate boundary
conditions), yields the desired solenoidal velocity vector. The method is
applied to the two- and three-dimensional problems for the homogeneous
Dirichlet, as well as periodic boundary conditions. The results show that the
solenoidality is satisfied up to the machine accuracy for the periodic boundary
conditions (employing the Fourier--spectral solution method), while an
improvement in the solenoidality is achievable for the homogenous boundary
conditions.
