  We propose an efficient threshold dynamics method for topology optimization
for fluids modeled with the Stokes equation. The proposed algorithm is based on
minimization of an objective energy function that consists of the dissipation
power in the fluid and the perimeter approximated by nonlocal energy, subject
to a fluid volume constraint and the incompressibility condition. We show that
the minimization problem can be solved with an iterative scheme in which the
Stokes equation is approximated by a Brinkman equation. The indicator functions
of the fluid-solid regions are then updated according to simple convolutions
followed by a thresholding step. We demonstrate mathematically that the
iterative algorithm has the total energy decaying property. The proposed
algorithm is simple and easy to implement. A simple adaptive time strategy is
also used to accelerate the convergence of the iteration. Extensive numerical
experiments in both two and three dimensions show that the proposed iteration
algorithm converges in much fewer iterations and is more efficient than many
existing methods. In addition, the numerical results show that the algorithm is
very robust and insensitive to the initial guess and the parameters in the
model.
