EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 47 / No 6 (November-December 2013) ESAIM: M2AN, 47 6 (2013) 1627-1655 References
Free Access
Issue
ESAIM: M2AN
Volume 47, Number 6, November-December 2013
Page(s) 1627 - 1655
DOI https://doi.org/10.1051/m2an/2013081
Published online 26 August 2013
  1. C. Ancey, Plasticity and geophysical flows: a review. J. Non-Newtonian Fluid. Mech. 142 (2007) 4–35. [Google Scholar]
  2. N.J. Balmforth and R.V. Craster, A consistent thin-layer theory for Bingham plastics. J. Non-Newtonian Fluid Mech. 84 (1999) 65–81. [CrossRef] [Google Scholar]
  3. N.J. Balmforth, R.V. Craster and R. Sassi, Shallow viscoplastic flow on an inclined plane. J. Fluid Mech. 420 (2002) 1–29. [Google Scholar]
  4. J. Banasiak and J.R. Mika, Asymptotic analysis of the Fokker–Planck equations related to Brownian motion. Math. Mod. Meth. Appl. S. 4 (1994) 17–33. [CrossRef] [Google Scholar]
  5. F. Bouchut and S. Boyaval, A new model for shallow elastic fluids. Preprint (2011), ArXiv:1110.0799[math.NA]. [Google Scholar]
  6. D. Bresch, E.D. Fernández-Nieto, I.R. Ionescu and P. Vigneaux, Augmented Lagrangian Method and Compressible Visco-plastic Flows: Applications to Shallow Dense Avalanches. Adv. Math. Fluid Mech. (2010) 57–89. Doi: 10.1007/978-3-0346-0152-84. [Google Scholar]
  7. D. Bresch and P. Noble, Mathematical justification of a shallow water model. Methods Appl. Anal. 14 (2007) 87–118. [CrossRef] [MathSciNet] [Google Scholar]
  8. E.C. Bingham, Fluidity and plasticity. Mc Graw-Hill (1922). [Google Scholar]
  9. R.B. Bird, C.F. Curtiss, R.C. Armstrong and O. Hassager, Dynamic polymeric liquids, in: Kinetic theory. John Wiley and Sons (1987). [Google Scholar]
  10. L. Chupin, The FENE model for viscoelastic thin film flows. Meth. Appl. Anal. 16 (2009) 217–262. [CrossRef] [Google Scholar]
  11. M. Boutounet, L. Chupin, P. Noble and J.-P. Vila, Shallow water viscous ßows for arbitrary topography. Commun. Math. Sci. 6 (2008) 29–55. [CrossRef] [Google Scholar]
  12. P. Degond, M. Lemou and M. Picasso, Viscoelastic fluid models derived from kinetic equations for polymers. SIAM J. Appl. Math. 62 (2002) 1501–1019. [CrossRef] [Google Scholar]
  13. E.D. Fernández-Nieto and G. Narbona-Reina, Extension of WAF Type Methods to Non-Homogeneous Shallow-Water Equations with Pollutant. J. Sci. Comput. 36 (2008) 193–217. [CrossRef] [Google Scholar]
  14. E.D. Fernández-Nieto, P. Noble and J.-P. Vila, Shallow Water equations for Non Newtonian fluids, J. Non-Newtonian Fluid Mech. 165 (2010) 712–732. [CrossRef] [Google Scholar]
  15. J.-F. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water, numerical validation. Discrete Contin. Dyn. Syst. Ser. B 1 (2001) 89–102. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Guala and A. Stocchino, Large-scale flow structures in particle-wall collision at low Deborah numbers. Eur. J. Mech. B/Fluids 26 (2007) 511–530. [CrossRef] [Google Scholar]
  17. O.G. Harlen, J.M. Rallison and M.D. Chilcott, High-Deborah-Number flows of dilute polymer solutions. J. Non-Newtorian Fluid Mech. 34 (1990) 319–349. [CrossRef] [Google Scholar]
  18. A. Harnoy, The relation between CMD instability and Deborah number in differential type rheological equations. Rheol. Acta 32 (1993) 483–489. [CrossRef] [Google Scholar]
  19. A. Harnoy, Bearing Design in Machinery Engineering Tribology and Lubrication. CRC Press (2002). [Google Scholar]
  20. W.H. Herschel and T. Bulkley, Measurement of consistency as applied to rubber-benzene solutions. Am. Soc. Test Proc. 26 (1926) 621–633. [Google Scholar]
  21. B. Jourdain, T. Lelièvre and C. Le Bris, Numerical analysis of micro-macro simulations of polymeric fluid flows: a simple case. Math. Mod. Meth. Appl. S 12 (2002) 1205–1243. [CrossRef] [Google Scholar]
  22. Y. Kwon, S.J. Kim and S. Kim, Finite element modeling of high Deborah number planar contration flows with rational function interpolation of the Leonov model. Korea-Australia Rheol. J. 15 (2003) 131–150. [Google Scholar]
  23. E. Lauga, Life at high Deborah number. Europhys. Lett. 86 (2009). Doi: 10.1209/0295-5075/86/64001. [Google Scholar]
  24. C. Le Bris, Systèmes multi-échelles: Modélisation et simulation. Springer-Verlag, Berlin (2005). [Google Scholar]
  25. T. Li, E. Vanden-Eijnden, P. Zhang and W. E, Stochastic models of polymeric fluids at small Deborah number. J. Non-Newtonian Fluid Mech. 121 (2004) 117–125. [CrossRef] [Google Scholar]
  26. F. Lin, P. Zhang and Z. Zhang, On the Global Existence of Smooth Solution to the 2-D FENE Dumbbell Model. Commun. Math. Phys. 277 (2008) 531–553. [CrossRef] [Google Scholar]
  27. A. Lozinski, R.G. Owens and G. Fang, A Fokker–Planck based numerical method for modelling non-homogeneous flows of dilute polymeric solutions. J. Non-Newtonian Fluid Mech. 122 (2004) 273–286. [CrossRef] [Google Scholar]
  28. F. Marche, Derivation of a new two-dimensional viscous shallow water model with varying topog- raphy, bottom friction and capillary effects, Eur. J. Mechanics-B/Fluids 26 (2007) 49–63. [CrossRef] [Google Scholar]
  29. N. Masmoudi, Well-Posedness for the FENE Dumbbell Model of Polymeric Flows. Commun. Pure Appl. Math. 61 (2008) 1685–1714. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Mellet and A. Vasseur, Asymptotic Analysis for a Vlasov-Fokker–Planck/Compressible Navier–Stokes System of Equations. Commun. Math. Phys. 281 (2008) 573–596. [CrossRef] [Google Scholar]
  31. G. Narbona-Reina and D. Bresch, On a shallow water model for non-newtonian fluids, Numer. Math. Adv. Appl. Springer Berlin, Heidelberg (2010) 693–701. [Google Scholar]
  32. G. Narbona-Reina, J.D. Zabsonré, E.D. Fernández-Nieto and D. Bresch, Derivation of a bilayer model for Shallow Water equations with viscosity. Numerical validation. CMES 43 (2009) 27–71. [Google Scholar]
  33. A. Oron, S.H. Davis and S.G. Bankoff, Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (1997) 931–980. [CrossRef] [Google Scholar]
  34. H.C. Ottinger, Stochastic Processes in Polymeric Fluids. Springer-Verlag, Berlin (1996). [Google Scholar]
  35. M. Reiner, The Deborah number, Phys. Today 12 (1964) 62. [CrossRef] [Google Scholar]
  36. S. Shao and E.Y.M. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Resources 26 (2003) 787–800. [CrossRef] [Google Scholar]
  37. J.A. Tichy and M.F. Modest, A Simple Low Deborah Numer Model for Unsteady Hydrodynamic Lubrication, Including Fluid Inertia. J. Rheology 24 (1980) 829–845. [CrossRef] [Google Scholar]
  38. E.F. Toro, Shock-Capturing Methods for Free-Surface Shallow Flows. John Wiley and Sons, England (2001). [Google Scholar]
  39. H. Zhang and P. Zhang, Local Existence for the FENE-Dumbbell Model of Polymeric Fluids. Arch. Ration. Mech. Anal. 181 (2006) 373–400. [CrossRef] [MathSciNet] [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