Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse

JOURNAL OF COMPUTATIONAL PHYSICS

卷:333

Article

Lusso, Christelle¹  Ern, Alexandre¹  Bouchut, Francois²  Mangeney, Anne^3,4  Farin, Maxime³  Roche, Olivier⁵ 

[1] Univ Paris Est, CERMICS ENPC, F-77455 Marne La Vallee 2, France

[2] Univ Paris Est, CNRS, Lab Anal & Math Appl, UMR 8050,UPEM,UPEC, F-77454 Marne La Vallee, France

[3] Univ Paris Diderot, Inst Phys Globe Paris, Seismol Grp, Sorbonne Paris Cite, 1 Rue Jussieu, F-75005 Paris, France

[4] INRIA, CETMEF, Lab J Louis Lions, ANGE Team, Paris, France

[5] Univ Blaise Pascal, CNRS, IRD, Lab Magma & Volcans,OPGC, Campus Cezeaux,6 Ave Blaise Pascal, F-63178 Aubiere, France

关键词: Viscoplastic flows;    Drucker-Prager pressure-dependent yield stress;    Free surface;    Regularization;    ALE method;    Granular collapse;   

DOI  :  10.1016/j.jcp.2016.12.036

来源: Elsevier

【 摘 要 】

This work is devoted to numerical modeling and simulation of granular flows relevant to geophysical flows such as avalanches and debris flows. We consider an incompressible viscoplastic fluid, described by a rheology with pressure-dependent yield stress, in a 2D setting with a free surface. We 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 Lagrangian Eulerian (ALE) formulation for the displacement of the domain. The free surface is evolved by taking care of its deposition onto the bottom and of preventing it from folding over itself. Several tests are performed to assess the efficiency of our method. The first test is dedicated to verify its accuracy and cost on a one-dimensional simple shear plug flow. On this configuration we setup rules for the choice of the numerical parameters. The second test aims to compare the results of our numerical method to those predicted by an augmented Lagrangian formulation in the case of the collapse and spreading of a granular column over a horizontal rigid bed. Finally 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. We compare the evolution of the free surface, the velocity profiles, and the static flowing interface. The results show the ability of our method to deal numerically with the front behavior of granular collapses over an erodible bed. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free