Two-dimensional continuum modelling granular column collapse by non-local peridynamics in a mesh-free method with rheology

2021 ◽  
Vol 917 ◽  
Author(s):  
Tibing Xu ◽  
Yee-Chung Jin
Keyword(s):  
Two Dimensional ◽  
Column Collapse ◽  
Mesh Free ◽  
Continuum Modelling ◽  
Mesh Free Method ◽  
Non Local ◽  
Granular Column

Abstract

scholarly journals A Numerical Method for SolvingTwo-Dimensional Nonlinear Parabolic ProblemsBased on a Preconditioning Operator

2020 ◽  
Vol 25 (4) ◽  
pp. 531-545
Author(s):  
Amir Hossein Salehi Shayegan ◽  
Ali Zakeri ◽  
Seyed Mohammad Hosseini
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parabolic Problem ◽  
Time Variable ◽  
Two Dimensional ◽  
Helmholtz Operator ◽  
Mesh Free ◽  
Nonlinear Parabolic ◽  
Spline Finite Element ◽  
Mesh Free Method

This article considers a nonlinear system of elliptic problems, which is obtained by discretizing the time variable of a two-dimensional nonlinear parabolic problem. Since the system consists of ill-conditioned problems, therefore a stabilized, mesh-free method is proposed. The method is based on coupling the preconditioned Sobolev space gradient method and WEB-spline finite element method with Helmholtz operator as a preconditioner. The convergence and error analysis of the method are given. Finally, a numerical example is solved by this preconditioner to show the efficiency and accuracy of the proposed methods.

Generalized-strain mesh-free method (GSMF) for two-dimensional elasticity problems

2017 ◽  
Author(s):  
Wilber Vélez ◽  
Tiago da Silva Oliveira ◽  
Elvis Pereira de Santana ◽  
Artur Portela
Keyword(s):  
Two Dimensional ◽  
Mesh Free ◽  
Mesh Free Method ◽  
Elasticity Problems

The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a μ(I)-rheology

2011 ◽  
Vol 686 ◽  
pp. 378-408 ◽  
Author(s):  
P.-Y. Lagrée ◽  
L. Staron ◽  
S. Popinet
Keyword(s):  
Analytical Solutions ◽  
Granular Layer ◽  
Contact Dynamics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Numerical Work ◽  
Aspect Ratios ◽  
Column Collapse ◽  
Wide Range ◽  
Granular Column

AbstractThere is a large amount of experimental and numerical work dealing with dry granular flows (such as sand, glass beads, etc.) that supports the so-called $\ensuremath{\mu} (I)$-rheology. The reliability of the $\ensuremath{\mu} (I)$-rheology in the case of complex transient flows is not fully ascertained, however. From this perspective, the granular column collapse experiment provides an interesting benchmark. In this paper we implement the $\ensuremath{\mu} (I)$-rheology in a Navier–Stokes solver (Gerris) and compare the resulting solutions with both analytical solutions and two-dimensional contact dynamics discrete simulations. In a first series of simulations, we check the numerical model in the case of a steady infinite two-dimensional granular layer avalanching on an inclined plane. A second layer of Newtonian fluid is then added over the granular layer in order to recover a close approximation of a free-surface condition. Comparisons with analytical and semi-analytical solutions provide conclusive validation of the numerical implementation of the $\ensuremath{\mu} (I)$-rheology. In a second part, we simulate the unsteady two-dimensional collapse of granular columns over a wide range of aspect ratios. Systematic comparisons with discrete two-dimensional contact dynamics simulations show good agreement between the two methods for the inner deformations and the time evolution of the shape during most of the flow, while a systematic underestimation of the final run-out is observed. The experimental scalings of spreading of the column as a function of the aspect ratio available from the literature are also recovered. A discussion follows on the performances of other rheologies, and on the sensitivity of the simulations to the parameters of the $\ensuremath{\mu} (I)$-rheology.

scholarly journals A New Granular Column Collapse Device to Characterise Flowability of Bulk Materials

Proceedings ◽  
2018 ◽  
Vol 2 (8) ◽  
pp. 488 ◽  
Author(s):  
Joel Torres-Serra ◽  
Enrique Romero ◽  
Antonio Rodríguez-Ferran
Keyword(s):  
Bulk Materials ◽  
Column Collapse ◽  
Granular Column
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