Free Access
Volume 47, Number 6, November-December 2013
Page(s) 1627 - 1655
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]

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