WIAS Preprint No. 2040, (2014)

A Stokes-consistent backflow stabilization for physiological flows


  • Bertoglio, Cristobal
  • Caiazzo, Alfonso
    ORCID: 0000-0002-7125-8645

2010 Mathematics Subject Classification

  • 62P10 76D05 76M10, 76Z05

2008 Physics and Astronomy Classification Scheme

  • 47.63.-b, 47.11.-j


  • Navier-Stokes equations, backflow stabilization, blood flows, respiratory flows, finite element method


In computational fluid dynamics incoming flow at open boundaries, or emphbackflow, 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 empha 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.

Appeared in

  • J. Comput. Phys., 313 (2016) pp. 260--278.

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