Free Access
Volume 50, Number 2, March-April 2016
Page(s) 565 - 591
Published online 14 March 2016
  1. J.C. Adams, mudpack: Multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations. Appl. Math. Comput. 34 (1989) 113–146. [CrossRef] [Google Scholar]
  2. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Academic Press (2003). [Google Scholar]
  3. S. Agmon, Lectures on Elliptic Boundary Value Problems. Prepared for Publication by B. Frank Jones, with the Assistance of George W. Batten (1965). [Google Scholar]
  4. Ph. Angot, Analysis of singular perturbations on the brinkman problem for fictitious domain models of viscous flowsh. Math. Methods Appl. Sci. 22 (1999) 1395–1412. [Google Scholar]
  5. Ph. Angot, Ch.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81 (1999) 497–520. [CrossRef] [MathSciNet] [Google Scholar]
  6. G.J. Besseris and D.B. Yeates, Rotating magnetic particle microrheometry in biopolymer fluid dynamics: Mucus microrheology. J. Chem. Phys. 127 (2007) 105106–105106. [CrossRef] [PubMed] [Google Scholar]
  7. C. Bost, G.-H. Cottet and E. Maitre, Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid. SIAM J. Numer. Anal. 48 (2010) 1313–1337. [Google Scholar]
  8. F. Boyer and P. Fabrie, Eléments d’analyse pour l’étude de quelques modèles d’écoulements de fluides visqueux incompressibles. Springer (2005). [Google Scholar]
  9. G. Carbou and P. Fabrie, Boundary layer for a penalization method for viscous incompressible flow. Adv. Differ. Eq. 8 (2003) 1453–1480. [Google Scholar]
  10. R. Chatelin, Méthodes numériques pour l’écoulement de Stokes 3D: fluides à viscosité variable en géométrie complexe mobile; application aux fluides biologiques. Ph.D. thesis, Université Toulouse 3 Paul Sabatier (2013). [Google Scholar]
  11. R. Chatelin and Ph. Poncet, A hybrid grid-particle method for moving bodies in 3D stokes flow with variable viscosity. SIAM J. Sci. Comput. 35 (2013) B925–B949. [CrossRef] [Google Scholar]
  12. R. Chatelin and Ph. Poncet, Hybrid grid–particle methods and penalization: A Sherman–Morrison–Woodbury approach to compute 3D viscous flows using FFT. J. Comput. Phys. 269 (2014) 314–328. [CrossRef] [Google Scholar]
  13. G.-H. Cottet and P. Poncet, Advances in direct numerical simulations of 3D wall-bounded flows by vortex-in-cell methods. J. Comput. Phys. 193 (2004) 136–158. [CrossRef] [Google Scholar]
  14. M. Coquerelle and G.-H. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies. J. Comput. Phys. 227 (2008) 9121–9137. [CrossRef] [Google Scholar]
  15. G.-H. Cottet and P.D. Koumoutsakos, Vortex Methods: Theory and Practice. Cambridge University Press (2000). [Google Scholar]
  16. R.V. Craster and O.K. Matar, Surfactant transport on mucus films. J. Fluid Mech. 425 (2000) 235–258. [CrossRef] [Google Scholar]
  17. R. Dautray and J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 1−6. Springer (2000). [Google Scholar]
  18. G. Duvaut and J.L. Lions, Les inéquations en mécanique et en physique (1972). [Google Scholar]
  19. P.A. Edwards and D.B. Yeates, Magnetic Rheometry of Bronchial Mucus. In vol. 489 of Viscoelasticity of Biomaterials, ACS Symposium Series. American Chemical Society (1992) 249–267. [Google Scholar]
  20. M. El Ossmani and P. Poncet, Efficiency of multiscale hybrid grid-particle vortex methods. Multiscale Model. Simul. 8 (2010) 1671–1690. [CrossRef] [Google Scholar]
  21. C. Foias and R. Temam, Remarques sur les équations de navier-stokes stationnaires et les phénomènes successifs de bifurcation. Ann. Sc. Norm. Super. Pisa - Cl. Sci. 5 (1978) 29–63. [Google Scholar]
  22. R. Glowinski, T.-W. Pan, T.I. Hesla and D.D. Joseph, A distributed lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow 25 (1999) 755–794. [CrossRef] [Google Scholar]
  23. G. Hou, J. Wang and A. Layton, Numerical methods for fluid-structure interaction – a review. Commun. Comput. Phys. 12 (2012) 337–377. [Google Scholar]
  24. H.H. Hu, Direct simulation of flows of solid-liquid mixtures. Int. J. Multiphase Flow 22 (1996) 335–352. [Google Scholar]
  25. J. Hussong, N. Schorr, J. Belardi, O. Prucker, J. Rhe and J. Westerweel, Experimental investigation of the flow induced by artificial cilia. Lab on a Chip 11 (2011) 2017–2022. [CrossRef] [PubMed] [Google Scholar]
  26. J. Hussong, W.-P. Breugem and J. Westerweel, A continuum model for flow induced by metachronal coordination between beating cilia. J. Fluid Mech. 684 (2011) 137–162. [CrossRef] [Google Scholar]
  27. J. Janela, A. Lefebvre and B. Maury. A penalty method for the simulation of fluid-rigid body interaction. ESAIM: Procs. 14 (2005) 115–123. [Google Scholar]
  28. M. Krotkiewski, I.S. Ligaarden, K.-A. Lie and D.W. Schmid, On the importance of the stokes-brinkman equations for computing effective permeability in karst reservoirs. Commun. Comput. Phys. 10 (2011) 1315–1332. [Google Scholar]
  29. A. Lefebvre, Fluid-particle simulations with FreeFem++. ESAIM: Procs. 18 (2007) 120–132. [CrossRef] [EDP Sciences] [Google Scholar]
  30. J.L. Lions-Magenes, Problèmes aux limites non homogènes et applications. In vol. 1 (1968). [Google Scholar]
  31. O.K. Matar, R.V. Craster and M.R.E. Warner, Surfactant transport on highly viscous surface films. J. Fluid Mech. 466 (2002) 85–111. [CrossRef] [Google Scholar]
  32. B. Maury, Direct simulations of 2D fluid-particle flows in biperiodic domains. J. Comput. Phys. 156 (1999) 325–351. [CrossRef] [MathSciNet] [Google Scholar]
  33. B. Maury, Numerical analysis of a finite element/volume penalty method. SIAM J. Numer. Anal. 47 (2009) 1126–1148. [CrossRef] [MathSciNet] [Google Scholar]
  34. S.M. Mitran, Metachronal wave formation in a model of pulmonary cilia. Comput. Struct. 85 (2007) 763–774. [CrossRef] [PubMed] [Google Scholar]
  35. J. Nečas, Les méthodes directes en théorie des équations elliptiques. Academia (1967). [Google Scholar]
  36. E. Puchelle, J.M. Zahm and C. Duvivier, Spinability of bronchial mucus. relationship with viscoelasticity and mucous transport properties. Biorheology 20 (1983) 239–249. PMID: 6871438. [PubMed] [Google Scholar]
  37. E. Puchelle, J.M. Zahm and D. Quemada, Rheological properties controlling mucociliary frequency and respiratory mucus transport. Biorheology 24 (1987) 557–563. PMID: 3502756. [PubMed] [Google Scholar]
  38. M.J. Sanderson and M.A. Sleigh, Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony. J. Cell Sci. 47 (1981) 331–347. [PubMed] [Google Scholar]
  39. D.J. Smith, E.A. Gaffney and J.R. Blake, Modelling mucociliary clearance. Respiratory Phys. Neurobiology 163 (2008) 178–188. [Google Scholar]
  40. D.J. Smith, E.A. Gaffney and J.R. Blake. A viscoelastic traction layer model of muco-ciliary transport. Bull. Math. Biology 69 (2007) 289–327. [CrossRef] [MathSciNet] [Google Scholar]
  41. P. Swarztrauber and R. Sweet, Efficient FORTRAN subprograms for the solution of elliptic partial differential equations (abstract). SIGNUM Newsl. 10 (1975). [Google Scholar]
  42. R.A. Sweet. A parallel and vector variant of the cyclic reduction algorithm. SIAM J. Sci. Statist. Comput. 9 (1988) 761–765. [CrossRef] [MathSciNet] [Google Scholar]
  43. M. Thiriet, Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems. In vol. 5 in Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems. Springer, Dordrecht (2012). [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