A Stokes-residual backflow stabilization method applied to physiological flows

In computational fluid dynamics, the presence of incoming flow at open boundaries (backflow) might often yield unphysical oscillations and instabilities issues, even for moderate Reynolds numbers. It is widely accepted that this problem is caused by the incoming convective energy at the open boundary, which cannot be controlled a priori when the velocity at the boundary is unknown. In this work, we propose a stabilized finite element formulation for the incompressible Navier-Stokes equations, in which the stabilization term is based on the residual of a weak Stokes problem normal to the open boundary, driven by an approximated boundary pressure gradient. In particular, the viscous term introduces additional dissipation which controls the incoming convective energy. This method has the advantage as it does not require modifications or extensions of the computational domain. Moreover, it does not require a priori assumptions on the shape of the boundary velocity field. We illustrate our approach through several numerical examples relevant to blood and respiratory flows, including Womersley flows and realistic geometries coming from medical imaging. The performance of the simulations is compared to recently reported approaches.