Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 2365 - 2419
DOI https://doi.org/10.1051/m2an/2021055
Published online 21 October 2021
  1. G. Arbia, I.E. Vignon-Clementel, T.-Y. Hsia and J.-F. Gerbeau. Modified Navier-Stokes equations for the outflow boundary conditions in hemodynamics. Eur. J. Mech. B Fluids 60 (2016) 175–188. [Google Scholar]
  2. L. Baffico, C. Grandmont and B. Maury. Multiscale modeling of the respiratory tract. Math. Models Methods Appl. Sci. 20 (2010) 59–93. [Google Scholar]
  3. Y. Bazilevs, J.R. Gohean, T.J.R. Hughes, R.D. Moser and Y. Zhang. Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput. Methods Appl. Mech. Engrg. 198 (2009) 3534–3550. [Google Scholar]
  4. C. Bertoglio and A. Caiazzo. A Stokes-residual backflow stabilization method applied to physiological flows. J. Comput. Phys. 313 (2016) 260–278. [Google Scholar]
  5. C. Bertoglio, A. Caiazzo, Y. Bazilevs, M. Braack, M. Esmaily, V. Gravemeier, A. Marsden, O. Pironneau, I.E. Vignon-Clementel and W.A. Wall. Benchmark problems for numerical treatment of backflow at open boundaries. Int. J. Numer. Meth. Biomed. Engng. 34 (2017) e2918. [Google Scholar]
  6. C. Bertoglio, A. Caiazzo and M.A. Fernández. Fractional-step schemes for the coupling of distributed and lumped models in hemodynamics. SIAM J. Sci. Comput. 35 (2013) B551–B575. [Google Scholar]
  7. P.J. Blanco, S. Deparis and A.C.I. Malossi. On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems. J. Comput. Phys. 251 (2013) 136–155. [Google Scholar]
  8. P.J. Blanco, M. Discacciati and A. Quarteroni. Modeling dimensionally-heterogeneous problems: analysis, approximation and applications. Numer. Math. 119 (2011) 299–335. [Google Scholar]
  9. P.J. Blanco, R.A. Feijóo and S.A. Urquiza. A unified variational approach for coupling 3D–1D models and its blood flow applications. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4391–4410. [Google Scholar]
  10. H. Brezis. Analyse fonctionnelle. Collection Mathématiques Appliquées pour la Ma trise. Masson, Paris (1983). [Google Scholar]
  11. C.-H. Bruneau and P. Fabrie. Effective downstream boundary conditions for incompressible Navier-Stokes equations. Int. J. Numer Meth. Fluids 19 (1994) 693–705. [Google Scholar]
  12. C.-H. Bruneau and P. Fabrie. New efficient boundary conditions for incompressible Navier-Stokes equations: a well-posedness result. RAIRO Modél. Math. Anal. Numér. 30 (1996) 815–840. [Google Scholar]
  13. A. Comerford, C. Forster and W.A. Wall. Structured tree impedance outflow boundary conditions for 3D lung simulations. J. Biomech. Eng. 132 (2010) 081002. [Google Scholar]
  14. A. Devys, C. Grandmont, B. Grec, B. Maury and D. Yakoubi. Numerical method for the 2D simulation of the respiration. In: CEMRACS 2008 – Modelling and numerical simulation of complex fluids. Vol. 28 of ESAIM Proc. EDP Sciences, Les Ulis (2009) 162–181. [Google Scholar]
  15. M. Esmaily Moghadam, Y. Bazilevs, T.-Y. Hsia, I.E. Vignon-Clementel, A.L. Marsden and Modeling of Congenital Hearts Alliance (MOCHA) Investigators. A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput. Mech. 48 (2011) 277–291. [Google Scholar]
  16. M. Esmaily Moghadam, F. Migliavacca, I.E. Vignon-Clementel, T.-Y. Hsia, A. Marsden and Modeling of Congenital Hearts Alliance (MOCHA) Investigators. Optimization of shunt placement for the Norwood surgery using multi-domain modeling. J. Biomech. Eng. 134 (2012) 051002. [Google Scholar]
  17. M. Esmaily Moghadam, I.E. Vignon-Clementel, R. Figliola and A.L. Marsden. A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations. J. Comput. Phys. 244 (2012) 63–79. [Google Scholar]
  18. L. Formaggia, A. Moura and F. Nobile. On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. ESAIM: M2AN 41 (2007) 743–769. [Google Scholar]
  19. L. Formaggia, A. Quarteroni, A. Veneziani. Cardiovascular Mathematics Modeling and simulation of the circulatory system. Springer-Verlag, Milan (2009). [Google Scholar]
  20. L. Formaggia, A. Quarteroni and C. Vergara. On the physical consistency between three-dimensional and one-dimensional models in haemodynamics. J. Comput. Phys. 244 (2013) 97–112. [Google Scholar]
  21. J. Fouchet-Incaux. Artificial boundaries and formulations for the incompressible Navier-Stokes equations: applications to air and blood flows. SeMA J. 64 (2014) 1–40. [Google Scholar]
  22. J. Fouchet-Incaux. Modélisation, analyse numérique et simulations autour de la respiration. Ph.D. thesis, Université Paris-Sud (2015). [Google Scholar]
  23. J. Fouchet-Incaux, C. Grandmont and S. Martin. Numerical stability of coupling schemes in the 3d/0d modelling of airflows and blood flows (2014). Preprint available at https://hal.inria.fr/hal-01095960/document [Google Scholar]
  24. T. Gengenbach, V. Heuveline and M.J. Krause. Numerical simulation of the human lung: A two-scale approach. EMCL 45 Preprint Ser. 29 2011–11 (2011). [Google Scholar]
  25. J.-F. Gerbeau, M. Vidrascu and P. Frey. Fluid-structure interaction in blood flows on geometries based on medical imaging. Comput. Struct. 83 (2005) 155–165. [Google Scholar]
  26. C. Grandmont, Y. Maday and B. Maury. A multiscale/multimodel approach of the respiration tree. New trends in continuum mechanics. In: Vol. 3 of Theta Series in Advanced Mathematics. Theta, Bucharest (2005) 147–157. [Google Scholar]
  27. C. Grandmont and A. Soualah. Solutions fortes des équations de Navier-Stokes avec conditions dissipatives naturelles. ESAIM Proc. 25 (2008) 1–18. [Google Scholar]
  28. V. Gravemeier, A. Comerford, L. Yoshihara, M. Ismail and W.A. Wall. A novel formulation for Neumann inflow boundary conditions in biomechanics. Int. J. Numer. Methods Biomed. Eng. 28 (2012) 560–573. [Google Scholar]
  29. J.G. Heywood and R. Rannacher. Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 19 (1982) 275–311. [Google Scholar]
  30. J.G. Heywood and R. Rannacher. Finite-element approximations of the nonstationary Navier-Stokes problem. part IV: Error estimates for second-order time discretization. SIAM J. Numer. Anal. 27 (1990) 353–384. [Google Scholar]
  31. J.G. Heywood, R. Rannacher and S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Eng. 22 (1996) 325–352. [Google Scholar]
  32. M. Ismail, A. Comerford and W.A. Wall. Coupled and reduced dimensional modeling of respiratory mechanics during spontaneous breathing. Int. J. Numer. Methods Biomed. Eng. 29 (2013) 1285–1305. [Google Scholar]
  33. M. Ismail, V. Gravemeier, A. Comerford and W.A. Wall. A stable approach for coupling multidimensional cardiovascular and pulmonary networks based on a novel pressure-flow rate or pressure-only Neumann boundary condition formulation. Int. J. Numer. Methods Biomed. Eng. 4 (2014) 447–469. [Google Scholar]
  34. C. Kleinstreuer, Z. Zhang, Z. Li, W.L. Roberts and C. Rojas. A new methodology for targeting drug-aerosols in the human respiratory system. Int. J. Heat Mass Transfer 51 (2008) 5578–5589. [Google Scholar]
  35. A.P. Kuprat, S. Kabilan, J.P. Carson, R.A. Corley and D.R. Einstein. A bidirectional coupling procedure applied to multiscale respiratory modeling. J. Comput. Phys. 244 (2013) 148–167. [Google Scholar]
  36. J.S. Leiva, P.J. Blanco and G.C. Buscaglia. Iterative strong coupling of dimensionally heterogeneous models. Internat. J. Numer. Methods Engrg. 81 (2010) 1558–1580. [Google Scholar]
  37. J.S. Leiva, P.J. Blanco and G.C. Buscaglia, Partitioned analysis for dimensionally-heterogeneous hydraulic networks. Multiscale Model. Simul. 9 (2011) 872–903. [Google Scholar]
  38. A.C.I. Malossi, P.J. Blanco, P. Crosetto, S. Deparis and A. Quarteroni. Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels. Multiscale Model. Simul. 11 (2013) 474–506. [Google Scholar]
  39. A.C.I. Malossi, P.J. Blanco, S. Deparis and A. Quarteroni. Algorithms for the partitioned solution of weakly coupled fluid models for cardiovascular flows. Int. J. Numer. Methods Biomed. Eng. 27 (2011) 2035–2057. [Google Scholar]
  40. B. Maury. The respiratory system in equations. In: Vol. 7 of MS&A: Modeling, Simulation and Applications. Springer-Verlag Italia, Milan (2013). [Google Scholar]
  41. V. Maz’ya and J. Rossmann. Point estimates for Green’s matrix to boundary value problems for second order elliptic systems in a polyhedral cone. ZAMM: Z. Angew. Math. Mech. 82 (2002) 291–316. [Google Scholar]
  42. V. Maz’ya and J. Rossmann. Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains. Math. Nachr. 280 (2007) 751–793. [Google Scholar]
  43. J.M. Oakes, A.L. Marsden, C. Grandmont, S.C. Shadden, C. Darquenne and I.E. Vignon-Clementel. Airflow and particle deposition simulations in health and emphysema: From in vivo to in silico animal experiments. Ann. Biomed. Eng. 42 (2014) 899–914. [Google Scholar]
  44. A. Porpora, P. Zunino, C. Vergara and M. Piccinelli. Numerical treatment of boundary conditions to replace lateral branches in hemodynamics. Int. J. Numer. Methods Biomed. Eng. 28 (2012) 1165–1183. [Google Scholar]
  45. A. Quarteroni, S. Ragni and A. Veneziani. Coupling between lumped and distributed models for blood flow problems. Comput. Visual Sci. 4 (2001) 111–124. [Google Scholar]
  46. A. Quarteroni and A. Veneziani. Modeling and simulation of blood flow problems, edited by M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J.-L. Lions, J. Periaux and M.F. Wheeler. In: Computational Science for the 21st Century. J. Wiley and Sons (1997) 369–379. [Google Scholar]
  47. A. Quarteroni and A. Veneziani. Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations. Multiscale Model. Simul. 1 (2003) 173–195. [Google Scholar]
  48. A. Quarteroni, A. Veneziani and C. Vergara. Geometric multiscale modeling of the cardiovascular system, between theory and practice. Comput. Methods Appl. Mech. Engrg. 302 (2016) 193–252. [Google Scholar]
  49. R. Temam. Navier-Stokes equations: theory and numerical analysis, Vol 2. American Mathematical Society (2001). [Google Scholar]
  50. A. Veneziani and C. Vergara. Flow rate defective boundary conditions in haemodynamics simulations. Inter. J. Numer. Methods Fluids 47 (2005) 803–816. [Google Scholar]
  51. I.E. Vignon-Clementel, C.A. Figueroa, K.E. Jansen and C.A. Taylor. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Engrg. 195 (2006) 3776–3796. [Google Scholar]
  52. W.A. Wall, L. Wiechert, A. Comerford and S. Rausch. Towards a comprehensive computational model for the respiratory system. Int. J. Numer. Methods Biomed. Eng. 26 (2010) 807–827. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you