We present a new methodology for the numerical resolution of the hydrodynamics
of incompressible viscid newtonian fluids. It is based on the Navier-Stokes
equations and we refer to it as the vorticity projection method.
The method is robust enough to handle complex and convoluted configurations
typical to the motion of biological structures in viscous fluids.
Although the method is applicable to three dimensions, we address here
in detail only the two dimensional case. We provide numerical data for
some test cases to which we apply the computational scheme.