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

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Abstract

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.

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Authors and Affiliations

  1. Mechanical and Aerospace Engineering Department, University of California, San Diego, USA

    Mahdi Esmaily Moghadam & Alison L. Marsden

  2. Structural Engineering Department, University of California, San Diego, USA

    Yuri Bazilevs

  3. Cardiac Unit, Institute of Child Health, Great Ormond Street Hospital for Children, London, UK

    Tain-Yen Hsia

  4. INRIA Paris-Rocquencourt, Rocquencourt, France

    Irene E. Vignon-Clementel

Authors
  1. Mahdi Esmaily Moghadam
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  2. Yuri Bazilevs
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  3. Tain-Yen Hsia
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  4. Irene E. Vignon-Clementel
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  5. Alison L. Marsden
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Modeling of Congenital Hearts Alliance (MOCHA)

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Correspondence to Yuri Bazilevs.

Additional information

MOCHA Investigators: Edward Bove MD and Adam Dorfman MD (University of Michigan, USA); Andrew Taylor MD, Alessandro Giardini MD, Sachin Khambadkone MD, Marc de Leval MD, Silvia Schievano PhD, and T-Y Hsia MD (Institute of Child Health, UK); G. Hamilton Baker MD and Anthony Hlavacek (Medical University of South Carolina, USA); Francesco Migliavacca PhD, Giancarlo Pennati PhD, and Gabriele Dubini PhD (Politecnico di Milano, Italy); Richard Figliola PhD and John McGregor PhD (Clemson University, USA); Alison Marsden PhD (University of California, San Diego, USA); Irene Vignon-Clementel (National Institute of Research in Informatics and Automation, France).

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Esmaily Moghadam, M., Bazilevs, Y., Hsia, TY. et al. A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput Mech 48, 277–291 (2011). https://doi.org/10.1007/s00466-011-0599-0

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  • DOI: https://doi.org/10.1007/s00466-011-0599-0

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