  A stabilized finite element method is introduced for the simulation of
time-periodic creeping flows, such as those found in the cardiorespiratory
systems. The new technique, which is formulated in the frequency rather than
time domain, strictly uses real arithmetics and permits the use of similar
shape functions for pressure and velocity for ease of implementation. It
involves the addition of the Laplacian of pressure to the continuity equation
with a complex-valued stabilization parameter that is derived systematically
from the momentum equation. The numerical experiments show the excellent
accuracy and robustness of the proposed method in simulating flows in complex
and canonical geometries for a wide range of conditions. The present method
significantly outperforms a traditional solver in terms of both computational
cost and scalability, which lowers the overall solution turnover time by
several orders of magnitude.
