  We present an immersed interface method for the vorticity-velocity form of
the 2D Navier Stokes equations that directly addresses challenges posed by
multiply connected domains, nonconvex obstacles, and the calculation of force
distributions on immersed surfaces. The immersed interface method is
re-interpreted as a polynomial extrapolation of flow quantities and boundary
conditions into the obstacle, reducing its computational and implementation
complexity. In the flow, the vorticity transport equation is discretized using
a conservative finite difference scheme and explicit Runge-Kutta time
integration. The velocity reconstruction problem is transformed to a scalar
Poisson equation that is discretized with conservative finite differences, and
solved using an FFT-accelerated iterative algorithm. The use of conservative
differencing throughout leads to exact enforcement of a discrete Kelvin's
theorem, which provides the key to simulations with multiply connected domains
and outflow boundaries. The method achieves second order spatial accuracy and
third order temporal accuracy, and is validated on a variety of 2D flows in
internal and free-space domains.
