However, we need to take into account the pressure-dependency of dry granular material ,
A constitutive law for dense granular ows, Nature, vol.441, p.727730, 2003. ,
DOI : 10.1038/nature04801
URL : http://arxiv.org/pdf/cond-mat/0612110
Les milieux granulaires : Entre uide et solide, 2011. ,
High-resolution radar measurements of snow avalanches, Geophysical Research Letters, vol.38, issue.18, p.727731, 2013. ,
DOI : 10.1016/S0165-232X(03)00060-0
Discrete element study mixing in an industrial sized mixer, Proc. World Congress Particle Technology 6, 2010. ,
Flows of Dense Granular Media, Annual Review of Fluid Mechanics, vol.40, issue.1, p.124, 2008. ,
DOI : 10.1146/annurev.fluid.40.111406.102142
URL : https://hal.archives-ouvertes.fr/hal-01432132
Granular matter: So much for the jamming point, Nature Physics, vol.22, issue.6, p.531532, 2016. ,
DOI : 10.1088/0951-7715/22/12/R01
On dense granular ows, The European Physical Journal E, vol.14, p.341365, 2004. ,
Rheophysics of pastes: a review of microscopic modelling approaches, Soft Matter, vol.93, issue.5, p.528540, 2007. ,
DOI : 10.1039/b611021p
Yield stress fluid flows: A review of experimental data, Journal of Non-Newtonian Fluid Mechanics, vol.211, pp.31-49, 2014. ,
DOI : 10.1016/j.jnnfm.2014.05.006
Numerical investigation of newtonian and non-newtonian multiphase ows using isph method, Computer methods in applied mechanics and engineering, vol.254, p.99113, 2013. ,
Viscoplastic modeling of granular column collapse with pressure-dependent rheology, Journal of Non-Newtonian Fluid Mechanics, vol.219, p.118, 2015. ,
DOI : 10.1016/j.jnnfm.2015.02.006
URL : https://hal.archives-ouvertes.fr/hal-01080456
The granular column collapse as a continuum: validity of a two-dimensional Navier???Stokes model with a ??(I)-rheology, Journal of Fluid Mechanics, vol.4, p.131, 2011. ,
DOI : 10.1088/0169-5983/41/6/065001
URL : https://hal.archives-ouvertes.fr/hal-01444545
Volume of uid (vof ) method for the dynamics of free boundaries, Journal of Computational Physics, vol.39, p.201225, 1981. ,
A smoothed two- and three-dimensional interface reconstruction method, Computing and Visualization in Science, vol.214, issue.7, pp.365-381, 2009. ,
DOI : 10.1007/s00791-008-0108-y
Diuse-interface methods in uid mechanics, Annual review of uid Mechanics, p.139165, 1998. ,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, p.1249, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
Level Set Methods: An Overview and Some Recent Results, Journal of Computational Physics, vol.169, issue.2, p.463502, 2001. ,
DOI : 10.1006/jcph.2000.6636
A hybrid extended nite element/level set method for modeling phase transformations, International journal for numerical methods in engineering, vol.54, p.12091233, 2002. ,
A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows, Journal of Computational Physics, vol.162, issue.2, pp.301-337, 2000. ,
DOI : 10.1006/jcph.2000.6537
A Hybrid Particle Level Set Method for Improved Interface Capturing, Journal of Computational Physics, vol.183, issue.1, p.83116, 2002. ,
DOI : 10.1006/jcph.2002.7166
Convected level set method for the numerical simulation of uid buckling, International journal for Numerical methods in Fluids, vol.66, p.324344, 2011. ,
A conservative level set method for two phase ow, Journal of Computational Physics, vol.210, p.225246, 2005. ,
Numerical simulations of bouncing jets, International Journal for Numerical Methods in Fluids, vol.29, issue.6, p.5375, 2015. ,
DOI : 10.1002/(SICI)1097-0363(19990330)29:6<705::AID-FLD809>3.0.CO;2-C
High delity anisotropic adaptive variational multiscale method for multiphase ows with surface tension, Computer methods in Applied Mechanics and Engineering, vol.307, p.4467, 2016. ,
Multiscale phenomena: Green's functions, the dirichlet-to-neumann formulation, subgrid scale models, bubbles and the origin of stabilized methods, Computer methods in applied mechanics and engineering, vol.127, p.387401, 1995. ,
The variational multiscale method -a paradigm for computational mechanics, Computer methods in applied mechanics and engineering, vol.166, p.324, 1998. ,
A multiscale discontinuous galerkin method with the computational structure of a continuous galerkin method, Computer methods in applied mechanics and engineering, vol.195, p.1922, 2006. ,
A stabilized mixed nite element method for darcy ow based on a multiscale decomposition of the solution, Computer methods in applied mechanics and engineering, vol.195, p.3336, 2006. ,
Immersed stress method for uid-structure interaction using anisotropic mesh adaptation, International journal for numerical methods in engineering, vol.94, p.805825, 2013. ,
Lagrangian shock hydrodynamics on tetrahedral meshed: a stable and accurate variational multiscale approach, Journal of Computational Physics, vol.231, p.80298069, 2012. ,
Stabilized stress-velocity-pressure nite element formulations of the navierstokes problem for uids with non-linear viscosity, Computer methods in applied mechanics and engineering, vol.279, p.554578, 2014. ,
Stabilized nite element method for incompressible ows with high reynolds number, Journal of Computational Physics, vol.229, p.86438665, 2010. ,
Comparison of some nite element methods for solving the diusion-convection-reaction equation, Computer methods in applied mechanics and engineering, p.185210, 1998. ,
A multiscale/stabilized formulation of the incompressible navierstokes equations for moving boundary ows and uidstructure interaction, Computational Mechanics, vol.38, p.403416, 2006. ,
Dynamic subscales in the nite element approximation of thermally coupled incompressible ows, Intenational Journal for Numerical Methods in Fluids, p.707730, 2007. ,
Metric construction by length distribution tensor and edge based error for anisotropic adaptive meshing, Journal of Computational Physics, vol.230, issue.7, p.23912405, 2011. ,
DOI : 10.1016/j.jcp.2010.11.041
URL : https://hal.archives-ouvertes.fr/hal-00579536
Adaptive time-step with anisotropic meshing for unsteady convection-diusion problems, Applied Mathematics Modelling, vol.39, p.18991916, 2015. ,
Edge residuals dominate a posteriori error estimates for linear nite element methods on anistropic triangular and tetrahedral meshes, Numerische Mathematik, vol.86, p.283303, 2000. ,
Collapse of a liquid column : numerical simulation and experimental validation, Computational Mechanics, 2007. ,
Solution of high-reynolds incompressible ow with stabilized nite element and adaptive anisotropic meshing, Computer methods in applied mechanics and engineering, vol.267, p.6585, 2013. ,
An adaptive nite element method for bingham uid ows around a cylinder, Computer methods in applied mechanics and engineering, vol.192, p.33173341, 2003. ,
Two???dimensional viscoplastic dambreaks, Journal of Non-Newtonian Fluid Mechanics, vol.238, 2016. ,
DOI : 10.1016/j.jnnfm.2016.05.008
Solution of the square lid-driven cavity ow of a bingham plastic using the nite volume method, Journal of Non-Newtonian Fluid Mechanics, vol.195, 1931. ,
A numerical study of the ow of bingham-like uids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics sph based method, Journal of Non-Newtonian Fluid Mechanics, vol.165, p.362375, 2010. ,
Laminar unsteady ows of bingham uids : a numerical strategy and some benchmark results, Journal of Computational Physics, vol.187, p.441456, 2003. ,
A regularized-stabilized miwed nite element formulation for viscoplasticity of bingham type, Computers and Mathematics with Applications, vol.66, p.975995, 2013. ,
nite-element method for incompressible non-newtonian ows, Journal of Computational Physics, vol.36, p.313326, 1980. ,
Flows of Materials with Yield, Journal of Rheology, vol.31, issue.5, p.385404, 1987. ,
DOI : 10.1122/1.549926
On the usage of viscosity regularisation methods for visco-plastic uid ow computation, Journal of Non-Newtonian Fluid Mechanics, vol.127, p.126, 2005. ,
A mixed formulation of the bingham uid ow problem : Analysis and numerical solution, Compuuters methods in applied mechanics and engineering, p.24342446, 2011. ,
Performance of the nite volume method in solving regularised bingham ows : Inertial eects in the lid-driven cavity ow, Journal of Non-Newtonian Fluid Mechanics, pp.208-209, 2014. ,
Stabilized mixed approximations for inertial viscoplastic uid ows, Mechanics Research Communications, vol.37, p.145152, 2010. ,
A 3rd order upwind nite volume method for generalised newtonian uid ows, Advances in Engineering Software, p.664680, 2005. ,
Very slow ow of bingham viscoplastic uid around a circular cylinder, Journal of Non-Newtonian Fluid Mechanics, vol.154, p.6576, 2008. ,
Adaptive variational multiscale method for bingham ows, Computers and Fluids, vol.138, p.5160, 2016. ,
Two-dimensional dam break ows of HerschelBulkley uids: The approach to the arrested state, Journal of Non-Newtonian Fluid Mechanics, vol.142, p.7994, 2007. ,
On a numerical strategy to compute gravity currents of nonnewtonian uids, Journal of Computational Physics, vol.201, p.397420, 2004. ,
Scaling laws for the slumping of a bingham plastic uid, Journal of Rheology, vol.57, 2013. ,
Spreading of a granular mass on a horizontal plane, Physics of Fluids, vol.63, issue.7, 2004. ,
DOI : 10.1016/S0013-7952(01)00090-4
Axisymmetric collapses of granular columns, Journal of Fluid Mechanics, vol.508, p.175199, 2004. ,
DOI : 10.1017/S0022112004009036
Granular collapse in two dimensions, Journal of Fluid Mechanics, vol.538, issue.-1, p.399428, 2005. ,
DOI : 10.1017/S0022112005005537
Collapses of two-dimensional granular columns, Physical Review E, vol.48, issue.4, 2005. ,
DOI : 10.1063/1.1870592
Continuum modeling and simulation of granular ows through their many phases, Journal of Fluid Mechanics, 2015. ,
A sph model for the simulation of free surface granular ows in a dense regime, Applied Mathematical Modelling, vol.39, p.363382, 2015. ,
Numerical simulations of granular free-surface flows using smoothed particle hydrodynamics, Journal of Non-Newtonian Fluid Mechanics, vol.166, issue.12-13, pp.698-712, 2011. ,
DOI : 10.1016/j.jnnfm.2011.03.007
A three-dimensional numerical model for dense granular ows based on the µ(i) rheology, Journal of Computational Physics, vol.256, p.696712, 2013. ,
Well-posed and ill-posed behaviour of the µ(i)rheology for granular ows, Journal of Fluid Mechanics, vol.779, p.794818, 2015. ,
Raining into shallow water as a description of the collapse of a column of grains, Journal of Fluid Mechanics, vol.554, issue.-1, p.259270, 2006. ,
DOI : 10.1017/S0022112005007974