A Stokes-consistent backflow stabilization for physiological flows

In computational fluid dynamics incoming flow at open boundaries, or \emph{backflow}, often yields to unphysical instabilities for high Reynolds numbers. It is widely accepted that this is due to the incoming energy arising from the convection term, which cannot be \emph{a priori} controlled when the velocity field is unknown at the boundary. In order to improve the robustness of the numerical simulations, we propose a stabilized formulation based on a penalization of the residual of a weak Stokes problem on the open boundary, whose viscous part controls the incoming convective energy, while the inertial term contributes to the kinetic energy. We also present different strategies for the approximation of the boundary pressure gradient, which is needed for defining the stabilization term. The method has the advantage that it does not require neither artificial modifications or extensions of the computational domain. Moreover, it is consistent with the Womersley solution. We illustrate our approach on numerical examples ~- both academic and real-life -~ relevant to blood and respiratory flows. The results also show that the stabilization parameter can be reduced with the mesh size

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

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