Computational Mechanics

, Volume 48, Issue 3, pp 277–291

A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations


  • Mahdi Esmaily Moghadam
    • Mechanical and Aerospace Engineering DepartmentUniversity of California
    • Structural Engineering DepartmentUniversity of California
  • Tain-Yen Hsia
    • Cardiac Unit, Institute of Child HealthGreat Ormond Street Hospital for Children
  • Irene E. Vignon-Clementel
    • INRIA Paris-Rocquencourt
  • Alison L. Marsden
    • Mechanical and Aerospace Engineering DepartmentUniversity of California
  • Modeling of Congenital Hearts Alliance (MOCHA)
Original Paper

DOI: 10.1007/s00466-011-0599-0

Cite this article as:
Esmaily Moghadam, M., Bazilevs, Y., Hsia, T. et al. Comput Mech (2011) 48: 277. doi:10.1007/s00466-011-0599-0


Simulation divergence due to backflow is a common, but not fully addressed, problem in three-dimensional simulations of blood flow in the large vessels. Because backflow is a naturally occurring physiologic phenomenon, careful treatment is necessary to realistically model backflow without artificially altering the local flow dynamics. In this study, we quantitatively compare three available methods for treatment of outlets to prevent backflow divergence in finite element Navier–Stokes solvers. The methods examined are (1) adding a stabilization term to the boundary nodes formulation, (2) constraining the velocity to be normal to the outlet, and (3) using Lagrange multipliers to constrain the velocity profile at all or some of the outlets. A modification to the stabilization method is also discussed. Three model problems, a short and long cylinder with an expansion, a right-angle bend, and a patient-specific aorta model, are used to evaluate and quantitatively compare these methods. Detailed comparisons are made to evaluate robustness, stability characteristics, impact on local and global flow physics, computational cost, implementation effort, and ease-of-use. The results show that the stabilization method offers a promising alternative to previous methods, with reduced effect on both local and global hemodynamics, improved stability, little-to-no increase in computational cost, and elimination of the need for tunable parameters.


Neumann boundary conditionsOutflow stabilizationLagrange multipliersNormal velocity constraintPatient-specific blood flowFlow reversalNavier–Stokes FEM solverCardiovascular simulation

Copyright information

© Springer-Verlag 2011