On Modeling Flow of a Large Deforming Porous Medium with Rate-Dependent Coulomb Friction Conditions

2010 ◽  
Author(s):  
E. Rohan ◽  
R. Cimrman
Keyword(s):  
Porous Medium ◽  
Coulomb Friction ◽  
Rate Dependent ◽  
Modeling Flow

scholarly journals Modeling flow in anisotropic porous medium with full permeability tensor

2019 ◽  
Vol 1324 ◽  
pp. 012054 ◽  
Author(s):  
Jie Cao ◽  
Hui Gao ◽  
Liangbin Dou ◽  
Ming Zhang ◽  
Tiantai Li
Keyword(s):  
Porous Medium ◽  
Permeability Tensor ◽  
Anisotropic Porous Medium ◽  
Modeling Flow

A non-primitive boundary element technique for modeling flow through non-deformable porous medium using Brinkman equation

Meccanica ◽  
2018 ◽  
Vol 53 (9) ◽  
pp. 2333-2352 ◽  
Author(s):  
Chandra Shekhar Nishad ◽  
Anirban Chandra ◽  
Timir Karmakar ◽  
G. P. Raja Sekhar
Keyword(s):  
Porous Medium ◽  
Boundary Element ◽  
Brinkman Equation ◽  
Deformable Porous Medium ◽  
Flow Through ◽  
Element Technique ◽  
Modeling Flow ◽  
Boundary Element Technique

scholarly journals Well-posed continuum equations for granular flow with compressibility and μ ( I )-rheology

2017 ◽  
Vol 473 (2201) ◽  
pp. 20160846 ◽  
Author(s):  
T. Barker ◽  
D. G. Schaeffer ◽  
M. Shearer ◽  
J. M. N. T. Gray
Keyword(s):  
Granular Flow ◽  
Coulomb Friction ◽  
Soil Mechanics ◽  
Rate Dependent ◽  
Continuum Modelling ◽  
Long Time ◽  
Two Dimensional Flow ◽  
Ill Posed ◽  
Coulomb Friction Law ◽  
Well Posed

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ ( I )-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I -dependent rheology. When the I -dependence comes from a specific friction coefficient μ ( I ), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ ( I ) satisfies certain minimal, physically natural, inequalities.

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