Bibliography

  • [A] Ch. Ancey. "Plasticity and geophysical flows: A review." Journal of Non-Newtonian Fluid Mechanics 142, 4 -  35 (2007).
  • [BeDeLu] L. Beznea, M. Deaconu, and O. Lupascu, Stochastic equation of fragmentation and branch-ing processes related to avalanches, Journal of Statistical Physics ing processes related to avalanches, Journal of Statistical Physics (2016).
  • [BFIV] D. Bresch, E. D. Fernandez-Nieto, I. R. Ionescu and P. Vigneaux. "Augmented Lagrangian Method and Compressible Visco-Plastic Flows : Applications to Shallow Dense Avalanches." New Directions in Mathematical Fluid Mechanics: The Alexander V. Kazhikhov Memorial Volume, A. V. Fursikov, G. P. Galdi and V. V. Pukhnachev (editors), Springer, 57-89, (2010).
  • [BFML] F. Bouchut, E. Fernandez-Nieto, A. Mangeney, and P. Y. Lagre. "On new erosion models of Savage-Hutter type for avalanches." Acta Mecha. 199, 198 - 208, (2008).
  • [BMPV] 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. Acad. Sci. Paris 336, 531-536, (2003).
  • [BIM16] F. Bouchut, I. R. Ionescu, and A. Mangeney, An analytic approach for the evolution of the static-flowing interface in viscoplastic granular flows, to appear in Communications in Mathematical Sciences (2016).
  • [CI06] Cazacu, O, Ionescu, IR Compressible rigid viscoplastic fluids, Journal of the Mechanics and Physics of Solids Volume: 54 Issue: 8 Pages: 1640-1667.
  • [FG] M. Fortin and R. Glowinski. "Methodes de Lagrangien augmentes, application a la resolution de problemes aux limites." Dunod (1982).
  • [DGG] E.J. Dean, R. Glowinski and G. Guidoboni. "On the numerical simulation of Bingham visco-plastic flow: old and new results." Journal of Non Newtonian Fluid Mechanics 142, 36-62, (2007).
  • [GlLT] R. Glowinski and P. Le Tallec. "Augmented Lagrangian and Operator Splitting method in Non-Linear Mechanics." SIAM Studies in Applied Mathematics (1989).
  • [HIL05] R. Hassani, L. R. Ionescu and T. Lachand-Robert. "Shape Optimization and Supremal Minimization Approaches in Landslides Modeling." Applied Mathematics and Optimization, 52, 349 - 364, (2005).
  • [I10] I. R. Ionescu. "Onset and dynamic shallow flow of a viscoplastic fluid on a plane slope." J. Non-Newtonian Fluid Mechanics 165, 1328-1341, (2010).
  • [I12] I. R. Ionescu. "Viscoplastic shallow flow equations with topography." Journal of Non-Newtonian Fluid Mechanics 193, 116-128, (2013).
  • [I13] I.R. Ionescu. "Augmented Lagrangian for shallow viscoplastic flow with topography." Journal of Computational Physics 242, 544 - 560, (2013).
  • [IMBR15] I. R. Ionescu, A. Mangeney, F. Bouchut and O. Roche, Viscoplastic modelling of granular column collapse with pressure dependent rheology, J. Non-Newtonian Fluid Mechanics, Vol. 219 (2015), 1-18.
  • [IL16] I. R. Ionescu and O. Lupascu, Modeling shallow avalanche onset over complex basal topography, Advances in Computational Mathematics, (DOI: 10.1007/s10444-015-9407-2 (2015).
  • [IL15] I. R. Ionescu, O. Lupascu, Onset of a dense avalanche on a plane slope, Proc. Romanian Academy-Series A, 16, 40-412 (2015).
  • [IL05] I. R. Ionescu and T. Lachand-Robert. "Generalized Cheeger sets related to landslides." Calculus of Variations and PDE, vol. 23, 227-249, (2005).
  • [IO] I.R. Ionescu and E. Oudet. "Discontinuous velocity domain splitting in limit analysis." Int. J. Solids and Structures 47, 1459-1468, (2010).
  • [ID01] R.M. Iverson and R.P. Denlinger. "Flow of variably fluidized granular masses across three-dimensional terrain: Coulomb mixture theory." J. Geophys. Res. 106 B1, 537- 552, (2001).
  • [JFP06] P. Jop, Y. Forterre and O. Pouliquen. "A constitutive law for dense granular flows."  Nature 441, 727-730, (2006).
  • [K] J.B. Keller. "Shallow-water theory for arbitrary slopes of the bottom." J. Fluid Mech. 489, 345-348, (2003).
  • [M03] A. Mageney-Castelneau, J.P. Villote, M.O. Bristeau, B. Perthame, F. Bochut, C. Simeoni and S. Yernei. "Numerical modeling of avalanches based on Saint-Venant equations using a kinetic scheme." J. Geophys. Res. 108 B11, 2527, (2003).
  • [M05] A. Mageney-Castelneau, F. Bochut, J.P. Villote, E. Lajeunesse, A. Aubertin and M. Pirulli. "On the Saint-Venant equations to simulate the spreading of a granular mass." J. Geophys. Res. 110 B9 B09103 (2005).
  • [PH] S. P. Pudasaini and K. Hutter. "Avalanche Dynamics - Dynamics of Rapid Flows of Dense Granular Avalanches." Springer (2007).
  • [PH03] S. P. Pudasaini and K. Hutter. "Rapid shear flows of dry granular masses down curved and twisted channels." J. Fluid Mech. 495, 193 -208, (2003).
  • [PHE03] S. P. Pudasaini, K. Hutter and W. Eckart. "Gravity driven rapid shear flows of dry granular masses in topographies with ortogonal and non-orthogonal metrics." In Dynamic response of granular and porous materials under large and catastrophic deformation, edited by K. Hunter and N. Kircher, Lecture Notes in Applied and Computational Mechanics 11, Springer, 43-82, (2003).
  • [SH89] S.B. Savage and K. Hutter. "The motion of a finite mass of granular material down a rough incline." Journal of Fluid Mechanics 199, 177-215, (1989).
  • [SH91] S.B. Savage and K. Hutter. "The dynamics of granular materials from initiation to runout." Acta Mechanica 86, 201- 223, (1991).
  • [WGH99] M. Wieland, J.M.N.T. Gray and K. Hunter. "Channelized free surfaces flow of cohesion less granular avalanches in a chute with shallow lateral curvature." J. Fluid Mech. 392, 73-100, (1999).
  • [WHP04] Y. Wang, K. Hutter and S.P. Pudasaini. "The Savage-Hutter theory: a system of partial differential equations for avalanche flow of snow, debris, and mud." ZAMM 84, 507-527, (2004).