Open Access
Issue
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S369 - S395
DOI https://doi.org/10.1051/m2an/2020042
Published online 26 February 2021
  1. C. Ancey and B.M. Bates, Stokes’ third problem for Herschel-Bulkley fluids. J. Non-Newtonian Fluid Mech. 243 (2017) 27–37. [Google Scholar]
  2. J.E. Andrade, Q. Chen, P.H. Le, C.F. Avila and T.M. Evans, On the rheology of dilative granular media: bridging solid- and fluid-like behavior. J. Mech. Phys. Solids 60 (2012) 1122–1136. [Google Scholar]
  3. A. Aradian, E. Raphael and P.-G. De Gennes, Surface flow of granular materials: a short introduction to some recent models. C. R. Phys. 3 (2002) 187–196. [Google Scholar]
  4. I.S. Aranson and L.S. Tsimring, Continuum theory of partially fluidized granular flows. Phys. Rev. E 65 (2002) 061303. [Google Scholar]
  5. I.S. Aranson, L.S. Tsimring, F. Malloggi and E. Clement, Nonlocal rheological properties of granular flows near a jamming limit. Phys. Rev. E 78 (2008) 031303. [Google Scholar]
  6. N.J. Balmforth and R.V. Craster, A consistent thin-layer theory for Bingham plastics. J. Non-Newtonian Fluid Mech. 84 (1999) 65–81. [Google Scholar]
  7. M. Barbolini, A. Biancardi, F. Cappabianca, L. Natale and M. Pagliardi, Laboratory study of erosion processes in snow avalanches. Cold Reg. Sci. Technol. 43 (2005) 1–9. [Google Scholar]
  8. T. Barker and J.M.N.T. Gray, Partial regularisation of the incompressible μ(I)-rheology for granular flow. J. Fluid Mech. 828 (2017) 5–32. [Google Scholar]
  9. T. Barker, D.G. Schaeffer, P. Bohorquez and J.M.N.T. Gray, Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow. J. Fluid Mech. 779 (2015) 794–818. [Google Scholar]
  10. T. Barker, D.G. Schaeffer, M. Shearer and J.M.N.T. Gray, Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology. Proc. R. Soc. A 473 (2017) 20160846. [Google Scholar]
  11. J.-P. Bouchaud, M.E. Cates, J.R. Prakash and S.F. Edwards, A model for the dynamics of sandpile surface. J. Phys. Paris I 4 (1994) 1383–1410. [Google Scholar]
  12. F. Bouchut and M. Westdickenberg, Gravity driven shallow water models for arbitrary topography. Comm. Math. Sci. 2 (2004) 359–389. [Google Scholar]
  13. F. Bouchut, A. Mangeney-Castelnau, B. Perthame and J.-P. Vilotte, A new model of Saint Venant and Savage-Hutter type for gravity driven shallow water flows. C. R. Math. Acad. Sci. Paris 336 (2003) 531–536. [Google Scholar]
  14. F. Bouchut, E. Fernandez-Nieto, A. Mangeney and P.-Y. Lagrée, On new erosion models of Savage-Hutter type for avalanches. Acta Mech. 199 (2008) 181–208. [Google Scholar]
  15. F. Bouchut, I.R. Ionescu and A. Mangeney, An analytic approach for the evolution of the static/flowing interface in viscoplastic granular flows. Comm. Math. Sci. 14 (2016) 2101–2126. [Google Scholar]
  16. T. Boutreux, E. Raphael and P.-G. DeGennes, Surface flows of granular materials: a modified picture for thick avalanches. Phys. Rev. E 58 (1998) 4692–4700. [Google Scholar]
  17. H. Capart, C.-Y. Hung and C.P. Stark, Depth-integrated equations for entraining granular flows in narrow channels. J. Fluid Mech. 765 (2015) R4. [Google Scholar]
  18. J. Chauchat and M. Médale, A three-dimensional numerical model for dense granular flows based on the μ(I) rheology. J. Comput. Phys. 256 (2014) 696–712. [Google Scholar]
  19. D.C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10 (1952) 157–165. [Google Scholar]
  20. R. Delannay, A. Valance, A. Mangeney, O. Roche and P. Richard, Granular and particle-laden flows: from laboratory experiments to field observations. J. Phys. D: Appl. Phys. 50 (2017) 053001. [Google Scholar]
  21. S. Douady, B. Andreotti and A. Daerr, On granular surface flow equations. Eur. Phys. J. B 11 (1999) 131–142. [CrossRef] [EDP Sciences] [Google Scholar]
  22. A.N. Edwards and J.M.N.T. Gray, Erosion-deposition waves in shallow granular free-surface flows. J. Fluid Mech. 762 (2015) 35–67. [Google Scholar]
  23. M. Farin, A. Mangeney and O. Roche, Fundamental changes of granular flow dynamics, deposition, and erosion processes at high slope angles: insights from laboratory experiments. J. Geophys. Res. Earth Surf. 119 (2014) 504–532. [Google Scholar]
  24. E.D. Fernandez-Nieto, J. Garres-Diaz, A. Mangeney and G. Narbona-Reina, A multilayer shallow model for dry granular flows with the μ(I) rheology: application to granular collapse on erodible beds. J. Fluid. Mech. 798 (2016) 643–681. [Google Scholar]
  25. J.M.N.T. Gray, Granular flow in partially filled slowly rotating drums. J. Fluid Mech. 441 (2001) 1–29. [Google Scholar]
  26. J.M.N.T. Gray and A.N. Edwards, A depth-averaged μ(I)-rheology for shallow granular free-surface flows. J. Fluid Mech. 755 (2014) 503–534. [Google Scholar]
  27. I.R. Ionescu, A. Mangeney, F. Bouchut and O. Roche, Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J. Non-Newtonian Fluid Mech. 219 (2015) 1–18. [Google Scholar]
  28. R.M. Iverson, Elementary theory of bed-sediment entrainment by debris flows and avalanches. J. Geophys. Res. 117 (2012) F03006. [Google Scholar]
  29. R.M. Iverson, C. Ouyang, Entrainment of bed material by Earth-surface mass flows: review and reformulation of depth-integrated theory. Rev. Geophys. 53 (2015) 27–58. [Google Scholar]
  30. P. Jop, Y. Forterre and O. Pouliquen, Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541 (2005) 167–192. [Google Scholar]
  31. P. Jop, Y. Forterre and O. Pouliquen, A constitutive law for dense granular flows. Nature 441 (2006) 727–730. [CrossRef] [PubMed] [Google Scholar]
  32. D.V. Khakhar, A.V. Orpe, P. Andresen and J.M. Ottino, Surface flow of granular materials: model and experiments in heap formation. J. Fluid Mech. 441 (2001) 225–264. [Google Scholar]
  33. P.-Y. Lagrée, L. Staron and S. Popinet, The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes model with a μ(I)-rheology. J. Fluid Mech. 686 (2011) 378–408. [Google Scholar]
  34. J.-L. Lions, Remarks on some nonlinear evolution problems arising in Bingham flows. Proc. Int. Symp. Partial Differ. Equ. Geom. Normed Linear Spaces (Jerusalem, 1972) Isr. J. Math. 13 (1972) 155–172. [Google Scholar]
  35. C. Lusso, F. Bouchut, A. Ern and A. Mangeney, A free interface model for static/flowing dynamics in thin-layer flows of granular materials with yield: simple shear simulations and comparison with experiments. Appl. Sci. 7 (2017) 386. [Google Scholar]
  36. A. Mangeney, L.S. Tsimring, D. Volfson, I.S. Aranson and F. Bouchut, Avalanche mobility induced by the presence of an erodible bed and associated entrainment. Geophys. Res. Lett. 34 (2007) L22401. [Google Scholar]
  37. A. Mangeney, F. Bouchut, N. Thomas, J.-P. Vilotte and M.-O. Bristeau, Numerical modeling of self-channeling granular flows and of their levee/channel deposits. J. Geophys. Res. Earth Surf. 112 (2007) F02017. [Google Scholar]
  38. A. Mangeney, O. Roche, O. Hungr, N. Mangold, G. Faccanoni and A. Lucas, Erosion and mobility in granular collapse over sloping beds. J. Geophys. Res. Earth Surf. 115 (2010) F03040. [Google Scholar]
  39. A. Mangeney-Castelnau, F. Bouchut, J.-P. Vilotte, E. Lajeunesse, A. Aubertin and M. Pirulli, On the use of Saint Venant equations to simulate the spreading of a granular mass. J. Geophys. Res. Solid Earth 110 (2005) B09103. [Google Scholar]
  40. N. Martin, I.R. Ionescu, A. Mangeney, F. Bouchut and M. Farin, Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects. Phys. Fluids 29 (2017) 013301. [Google Scholar]
  41. GdR MIDI, On dense granular flows. Eur. Phys. J. E Soft. Matter 14 (2004) 341–365. [PubMed] [Google Scholar]
  42. S. Parez, E. Aharonov and R. Toussaint, Unsteady granular flows down an inclined plane. Phys. Rev. E 93 (2016) 042902. [CrossRef] [PubMed] [Google Scholar]
  43. E.B. Pitman, C.C. Nichita, A.K. Patra, A.C. Bauer, M. Bursik and A. Webb, A model of granular flows over an erodible surface. Discrete Continuous Dyn. Syst. – B 3 (2003) 589–599. [Google Scholar]
  44. S.B. Savage and K. Hutter, The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199 (1989) 177–215. [Google Scholar]
  45. D.G. Schaeffer, Instability in the evolution equations describing incompressible granular flow. J. Diff. Equ. 66 (1987) 19–50. [Google Scholar]
  46. D.G. Schaeffer, T. Barker, D. Tsuji, P. Gremaud, M. Shearer and J.M.N.T. Gray, Constitutive relations for compressible granular flow in the inertial regime. J. Fluid Mech. 874 (2019) 926–951. [Google Scholar]
  47. N. Taberlet, P. Richard, A. Valance, R. Delannay, W. Losert, J.M. Pasini and J.T. Jenkins, Super stable granular heap in thin channel. Phys. Rev. Lett. 91 (2003) 264301. [CrossRef] [PubMed] [Google Scholar]
  48. T. Trinh, P. Boltenhagen, R. Delannay and A. Valance, Erosion and deposition processes in surface granular flows. Phys. Rev. E 96 (2017) 042904. [PubMed] [Google Scholar]

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