Abonnement à la biblothèque: Guest
Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections
International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2013004259
pages 407-441


Abdessalem Nachit
ICJ UMR CNRS 5208, University of Lyon, 23, rue P. Michelon, 42023, Saint Etienne, France
Gregory P. Panasenko
Equipe d'Analise Numerique UMR CNRS 5585, University Gean Monnet 23 rue. P. Michelon 42023 St. Etienne, France
Abdelmalek Zine
Universite de Lyon, ICJ UMR 5208, Ecole Centrale de Lyon, 36 Av. Guy de Collongue 69134, Ecully, France


The method of asymptotic partial domain decomposition for thin tube structures (finite unions of thin cylinders) is revisited. Its application to the Newtonian and non-Newtonian flows in large systems of vessels is considered. The possibility of a parallelization of its algorithm is discussed for linear and nonlinear models.


  1. Agmon, S., Douglis, A., and Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. DOI: 10.1002/cpa.3160170104

  2. Bird, R. B., Armstrong, R. C., and Hassager, O., Dynamics of Polymeric Liquids.

  3. Brezzi, F. and Fortin, M., Mixed and Hybrid Finite Element Methods.

  4. Blanc, F., Gipouloux, O., Panasenko, G. P., and Zine, A. M., Asymptotic analysis and partial asymptotic decomposition of the domain for stokes equation in tube structure. DOI: 10.1142/S0218202599000609

  5. Galdi, G., Ranacher, R., Robertson, A., and Turek, S., Hemodynamical Flows Modelling, Analysis and Simulation.

  6. Hood, P. and Taylor, C., Navier Stokes equations using mixed interpolation.

  7. Jung, J., Lyczkowski, R. W., Panchal, C. P., and Hassanein, A., Multiphase hemodynamic simulation of pulsatile flow in a coronary artery. DOI: 10.1016/j.jbiomech.2005.06.023

  8. Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow.

  9. Litvinov, V. G., Motion of Non-Linear Viscous Fluid.

  10. Malek, J., Necas, J., Rokyta, M., and Ruzicka, M., Weak and Measure-Valued Solutions to Evolutionary PDEs. DOI: 10.1155/S1048953397000117

  11. Nazarov, S. A. and Plamenevskii, B. A., Elliptic Problems in Domains with Piecewise Smooth Boundaries.

  12. Panasenko, G. P., Multi-Scale Modeling for Structures and Composites.

  13. Panasenko, G. P., Asymptotic expansion of the solution of Navier-Stokes equation in a tube structure. DOI: 10.1016/S1251-8069(99)80041-6

  14. Panasenko, G. P., Partial asymptotic decomposition of domain: Navier-Stokes equation in tube structure. DOI: 10.1016/S1251-8069(99)80045-3

  15. Panasenko, G. P., Parallelization of the algorithm of asymptotic partial domain decomposition in thin tube structures. DOI: 10.1016/j.crme.2010.10.007

  16. Panasenko, G. P. and Viallon, M. C., The finite volume implementation of the partial asymptotic domain decomposition. DOI: 10.1080/00036810802282533