Numerical simulation of blood flows through a porous interface

Mathematical Modelling and Numerical Analysis

Volumn 42, Issue 6, 2008, Pages 961-990

  Fernández, Miguel A ^a   Gerbeau, Jean Frédéric ^a   Martin, Vincent ^b  

^a INRIA   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Blood flow; Fluid structure interaction; Sieve problem; Stabilized finite element; Stent; Terminal aneurysm

Indexed keywords

EID: 55049093969     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2008031     Document Type: Article

References (30)

1. G. Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II. Noncritical sizes of the holes for a volume distribution and a surface distribution of holes. Arch. Rational Mech. Anal. 113 (1991) 261-298.
2. J.L. Berry, A. Santamarina, J.E. Jr. Moore, S. Roychowdhury and W.D. Routh, Experimental and computational flow evaluation of coronary stents. Ann. Biomed. Eng. 28 (2000) 386-398.
3. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, Berlin (1991).
4. A. Brillard, Asymptotic flow of a viscous and incompressible fluid through a plane sieve, in Progress in partial differential equations: calculus of variations, applications (Pont-à-Mousson, 1991), Pitman Res. Notes Math. Ser. 267, Longman Sci. Tech., Harlow (1992) 158-172.
5. E. Burman and P. Hansbo, Edge stabilization for the generalized Stokes problem: a continuous interior penalty method. Comput. Methods Appl. Mech. Engrg. 195 (2006) 2393-2410.
6. D. Chapelle and K.J. Bathe, The finite element analysis of shell - Fundamentals. Springer-Verlag (2004).
7. P.G. Ciarlet, The finite element method for elliptic problems, Classics in Applied Mathematics 40. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2002). Reprint of the 1978 original [North-Holland, Amsterdam; MR0520174 (58 #25001)].
8. P. Clément, Approximation by finite element functions using local regularization. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér. 9(R-2) (1975) 77-84.
9. R. Codina and J. Blasco, A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation. Comput. Methods Appl. Mech. Engrg. 143 (1997) 373-391.
10. C. Conca, Étude d'un fluide traversant une paroi perforée, I. Comportement limite près de la paroi. J. Math. Pures Appl. 66 (1987) 1-43.
11. C. Conca, Étude d'un fluide traversant une paroi perforée, II. Comportement limite loin de la paroi. J. Math. Pures Appl. 66 (1987) 45-70.
12. C. Conca and M. Sepúlveda, Numerical results in the Stokes sieve problem. Rev. Internac. Métod. Numér. Cálc. Diseñ. Ingr. 5 (1989) 435-452.
13. A. Ern and J.-L. Guermond, Theory and practice of finite elements, Applied Mathematical Sciences 159. Springer-Verlag, New York (2004).
14. L. Formaggia, J.-F. Gerbeau, F. Nobile and A. Quarteroni, On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Engrg. 191 (2001) 561-582.
15. P. Frey, Yams: A fully automatic adaptive isotropic surface remeshing procedure. Technical report 0252, INRIA, Rocquencourt, France, Nov. (2001).
16. P. Frey, Medit: An interactive mesh visualisation software. Technical report 0253, INRIA, Rocquencourt, France, Dec. (2001).
17. J.-F. Gerbeau and M. Vidrascu, A quasi-Newton algorithm based on a reduced model for fluid structure problems in blood flows. ESAIM: M2AN 37 (2003) 631-647.
18. J.-F. Gerbeau, M. Vidrascu and P. Frey, Fluid-structure interaction in blood flows on geometries coming from medical imaging. Comput. Struct. 83 (2005) 155-165.
19. V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations - Theory and algorithms, Springer Series in Computational Mathematics 5. Springer-Verlag, Berlin (1986).
20. T.J.R. Hughes, L.P. Franca and M. Balestra, A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comp. Meth. App. Mech. Eng. 59 (1986) 85-99.
21. A. Quarteroni and L. Formaggia, Mathematical modelling and numerical simulation of the cardiovascular system, in Handbook of Numerical Analysis XII, North-Holland, Amsterdam (2004) 3-127.
22. S. Salmon, M. Thiriet and J.-F. Gerbeau, Medical image-based computational model of pulsatile flow in saccular aneurisms. ESAIM: M2AN 37 (2003) 663-679.
23. E. Sánchez-Palencia, Problèmes mathématiques liés à ĺcoulement d'un fluide visqueux à travers une grille, in Ennio De Giorgi colloquium (Paris, 1983), Res. Notes in Math. 125, Pitman, Boston, USA (1985) 126-138.
24. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54(190) (1990) 483-493.
25. D.A. Steinman, J.S. Milner, C.J. Norley, S.P. Lownie and D.W. Holdsworth, Image-based computational simulation of flow dynamics int a giant intracranial aneurysms. Am. J. Neuroradiol. 24 (2003) 559-566.
26. G.R. Stuhne and D.A. Steinman, Finite-element modeling of the hemodynamics of stented aneurysms. J. Biomech. Eng. 126 (2004) 382-387.
27. V. Thomée, Galerkin finite element methods for parabolic problems, Springer Series in Computational Mathematics 25. Springer-Verlag, Berlin, second edition (2006).
28. L. Tobiska and V. Verfurth, Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations. SIAM J. Numer. Anal. 33 (1996) 107-127.
29. 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.
30. N.T. Wang and A.L. Fogelson, Computational methods for continuum models of platelet aggregation. J. Comput. Phys. 151 (1999) 649-675.