@article{fdi:010069295,
  title = {{T}wo-dimensional simulation by regularization of free surface viscoplastic flows with {D}rucker-{P}rager yield stress and application to granular collapse},
  author = {{L}usso, {C}. and {E}rn, {A}. and {B}ouchut, {F}. and {M}angeney, {A}. and {F}arin, {M}. and {R}oche, {O}livier},
  editor = {},
  language = {{ENG}},
  abstract = {{T}his work is devoted to numerical modeling and simulation of granular flows relevant to geophysical flows such as avalanches and debris flows. {W}e consider an incompressible viscoplastic fluid, described by a rheology with pressure-dependent yield stress, in a 2{D} setting with a free surface. {W}e implement a regularization method to deal with the singularity of the rheological law, using a mixed finite element approximation of the momentum and incompressibility equations, and an arbitrary {L}agrangian {E}ulerian ({ALE}) formulation for the displacement of the domain. {T}he free surface is evolved by taking care of its deposition onto the bottom and of preventing it from folding over itself. {S}everal tests are performed to assess the efficiency of our method. {T}he first test is dedicated to verify its accuracy and cost on a one-dimensional simple shear plug flow. {O}n this configuration we setup rules for the choice of the numerical parameters. {T}he second test aims to compare the results of our numerical method to those predicted by an augmented {L}agrangian formulation in the case of the collapse and spreading of a granular column over a horizontal rigid bed. {F}inally we show the reliability of our method by comparing numerical predictions to data from experiments of granular collapse of both trapezoidal and rectangular columns over horizontal rigid or erodible granular bed made of the same material. {W}e compare the evolution of the free surface, the velocity profiles, and the static flowing interface. {T}he results show the ability of our method to deal numerically with the front behavior of granular collapses over an erodible bed.},
  keywords = {{V}iscoplastic flows ; {D}rucker-{P}rager pressure-dependent yield stress ; {F}ree surface ; {R}egularization ; {ALE} method ; {G}ranular collapse},
  booktitle = {},
  journal = {{J}ournal of {C}omputational {P}hysics},
  volume = {333},
  numero = {},
  pages = {387--408},
  ISSN = {0021-9991},
  year = {2017},
  DOI = {10.1016/j.jcp.2016.12.036},
  URL = {https://www.documentation.ird.fr/hor/fdi:010069295},
}