A time-parallel Stokes solver via a new stabilized spectral finite element formulation

A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the small vessels of 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 is mass conservative and significantly outperforms traditional techniques by lowering the cost of simulating creeping flows in complex geometries by several orders of magnitude.