On micro scale the constitutions of porous media are effected by other constitutions, so their behaviors are very complex and it is hard to derive theoretical formulations as well as to simulate on macro scale. For decades, in order to escape this complication, the phenomenological approaches in a field of multiscale methods have been extensively researched by many material scientists and engineers. Their theoretical approaches are based on the hierarchical multiscale methods using a priori knowledge on a smaller scale; however it has a drawback that an information loss can be occurred. Recently, according to a development of the core technologies of computer, the ways of multiscale are extended to a direct multiscale approach called the concurrent multiscale method. This approach is not necessary to deal with complex mathematical formulations, but it is noted as an important factor: development of computational coupling algorithms between constitutions in a porous medium. In this work, we attempt to develop coupling algorithms in different numerical methods finite element method (FEM), smoothed particle hydrodynamics (SPH) and discrete element method (DEM). Using this coupling algorithm, fluid flow, movement of solid particle, and contact forces between solid domains are computed via proposed discrete element which is based on SPH, FEM, and DEM. In addition, a mixed FEM on continuum level and discrete element model with SPH particles on discontinuum level is introduced, and proposed coupling algorithm is verified through numerical simulation.

References

References
1.
Hou
,
T. Y.
, and
Wu
,
X. H.
,
1997
, “
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
,”
J. Comput. Phys.
,
134
(
1
), pp.
169
189
.10.1006/jcph.1997.5682
2.
Schrefler
,
B. A.
,
Gawin
,
D.
, and
Pesavento
,
F.
,
2006
, “
A Multiphase Model for Concrete: Numerical Solutions and Industrial Applications
,”
Progress in Industrial Mathematics at ECMI 2004, Mathematics in Industry
,
8
, pp.
337
350
.10.1007/3-540-28073-1
3.
Kippe
,
V.
,
Aarnes
,
J. E.
, and
Lie
,
K. A.
,
2008
, “
A Comparison of Multiscale Methods for Elliptic Problems in Porous Media Flow
,”
Comput. Geosci.
,
12
(
3
), pp.
377
-398
.10.1007/s10596-007-9074-6
4.
Hajibeygi
,
H.
, and
Jenny
,
P.
,
2009
, “
Multiscale Finite-Volume Method for Parabolic Problems Arising From Compressible Multiphase Flow in Porous Media
,”
J. Comput. Phys.
,
228
(
14
), pp.
5129
5147
.10.1016/j.jcp.2009.04.017
5.
Zhang
,
P.
,
Wu
,
Q. B.
,
Pu
,
Y. B.
,
Jiang
,
G. L.
,
Zhan
,
J.
, and
Wang
,
Y. M.
,
2010
, “
Water Transfer Characteristics During Methane Hydrate Formation and Dissociation Processes Inside Saturated Sand
,”
J. Natural Gas Chem.
,
19
(
1
), pp.
71
76
.10.1016/S1003-9953(09)60034-7
6.
El Shamy
,
U.
, and
Zeghal
,
M.
,
2007
, “
A Micro-Mechanical Investigation of the Dynamic Response and Liquefaction of Saturated Granular Soils
,”
Soil Dyn. Earthquake Eng.
,
27
(
8
), pp.
712
729
.10.1016/j.soildyn.2006.12.010
7.
Zeghal
,
M.
, and
El Shamy
,
U.
,
2008
, “
Liquefaction of Saturated Loose and Cemented Granular Soils
,”
Powder Technol.
,
184
(
2
), pp.
254
265
.10.1016/j.powtec.2007.11.032
8.
Elmekati
,
A.
, and
El Shamy
,
U.
,
2010
, “
A Practical Co-Simulation Approach for Multiscale Analysis of Geotechnical Systems
,”
Comput. Geotech.
,
37
(
4
), pp.
494
503
.10.1016/j.compgeo.2010.02.002
9.
Shafipour
,
R.
, and
Soroush
,
A.
,
2008
, “
Fluid Coupled-DEM Modelling of Undrained Behavior of Granular Media
,”
Comput. Geotech.
,
35
(
5
), pp.
673
685
.10.1016/j.compgeo.2007.12.003
10.
Muguruma
,
Y.
,
Tanaka
,
T.
, and
Tsuji
,
Y.
,
2000
, “
Numerical Simulation of Particulate Flow With Liquid Bridge Between Particles (Simulation of Centrifugal Tumbling Granulator)
,”
Powder Technol.
,
109
(
1–3
), pp.
49
57
.10.1016/S0032-5910(99)00226-0
11.
Soulie
,
F.
,
Cherblanc
,
F.
,
El Youssoufi
,
M. S.
, and
Saix
,
C.
,
2006
, “
Influence of Liquid Bridges on the Mechanical Behaviour of Polydisperse Granular Materials
,”
Int. J. Numer. Anal. Meth. Geomech.
,
30
(
3
), pp.
213
228
.10.1002/nag.476
12.
Abu Bakar
,
N. F.
,
Anzai
,
R.
, and
Horio
,
M.
,
2009
, “
Direct Measurement of Particle Interaction Using Micro Particle Interaction Analyzer (MPIA)
,”
Adv. Powder Technol.
,
20
(
5
), pp.
455
463
.10.1016/j.apt.2009.03.007
13.
El
Shamy
,
U.
, and
Groger
,
T.
,
2008
, “
Micromechanical Aspects of the Shear Strength of Wet Granular Soils
,”
Int. J. Numer. Anal. Meth. Geomech.
,
32
(
14
), pp.
1763
1790
.10.1002/nag.695
14.
Scholtes
,
L.
,
Hicher
,
P. Y.
,
Nicot
,
F.
,
Chareyre
,
B.
, and
Darve
,
F.
,
2009
, “
On the Capillary Stress Tensor in Wet Granular Materials
,”
Int. J. Numer. Anal. Meth. Geomech.
,
33
(
10
), pp.
1289
1313
.10.1002/nag.767
15.
Tartakovsky
,
A.
, and
Meakin
,
P.
,
2005
, “
Modeling of Surface Tension and Contact Angles With Smoothed Particle Hydrodynamics
,”
Phys. Rev. E
,
72
(
2
), pp.
1
9
.10.1103/PhysRevE.72.026301
16.
Tartakovsky
,
A. M.
, and
Meakin
,
P.
,
2006
, “
Pore Scale Modeling of Immiscible and Miscible Fluid Flows Using Smoothed Particle Hydrodynamics
,”
Adv. Water Res.
,
29
(
10
), pp.
1464
1478
.10.1016/j.advwatres.2005.11.014
17.
Tartakovsky
,
A. M.
,
Meakin
,
P.
,
Scheibe
,
T. D.
, and
West
,
R. M. E.
,
2007
, “
Simulations of Reactive Transport and Precipitation With Smoothed Particle Hydrodynamics
,”
J. Comput. Phys.
,
222
(
2
), pp.
654
672
.10.1016/j.jcp.2006.08.013
18.
Li
,
X.
,
Chu
,
X.
, and
Sheng
,
D. C.
,
2007
, “
A Saturated Discrete Particle Model and Characteristic-Based SPH Method in Granular Materials
,”
Int. J. Numer. Meth. Eng.
,
72
(
7
), pp.
858
882
.10.1002/nme.2037
19.
Berry
,
R. A.
,
Martineau
,
R. C.
, and
Wood
,
T. R.
,
2004
, “
Particle-Based Direct Numerical Simulation of Contaminant Transport and Deposition in Porous Flow
,”
Vadose Zone J.
,
3
(
1
), pp.
164
169
.10.2113/3.1.164
20.
Biot
,
M.
,
1941
, “
General Theory of Three Dimensional Consolidation
,”
J. Appl. Phys.
,
12
, pp.
155
164
.10.1063/1.1712886
21.
Terzaghi
,
K.
,
1925
,
Erdbaumechanik auf Bodenphysikalischer Grundlage
,
Leipzig u. Wien, F. Deuticke
,
Germany
.
22.
Lewis
,
R.
, and
Schrefler
,
B.
,
2000
,
The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media
,
Wiley
,
New York
.
23.
Cundall
,
P.
, and
Strack
,
O.
,
1979
, “
A Discrete Numerical Model for Granular Assemblies
,”
Geotechnique
,
29
(
1
), pp.
47
65
.10.1680/geot.1979.29.1.47
24.
Rojek
,
J.
, and
Õnate
,
E.
,
2007
, “
Multiscale Analysis Using a Coupled Discrete/Finite Element Model
,”
Interaction and Multiscale Mechanics
,
1
, pp.
1
31
.
25.
Hertz
,
H.
,
1826
, “
Über die Berührung fester elastischer Körper
,”
Journal für die reine und angewandte Mathematik
,
92
, pp.
156
171
.
26.
Morris
,
J.
,
1966
,
Analysis of Smoothed Particle Hydrodynamics With Applications
, PhD thesis, Monash University, Melbourne, Australia.
27.
Monaghan
,
J.
, and
Lattanzio
,
J.
,
1985
, “
A Refined Particle Method for Astrophysical Problems
,”
Astron. Astrophys.
,
149
, pp.
135
143
.
28.
Park
,
T.
, and
Tak
,
M.
,
2010
, “
A New Coupled Analysis for Nearly Incompressible and Impermeable Saturated Porous Media on Mixed Finite Element Method: I. Proposed Method
,”
KSCE J. Civil Eng.
,
14
(
1
), pp.
7
16
.10.1007/s12205-010-0007-x
29.
Tak
,
M.
, and
Park
,
T.
,
2010
, “
A New Coupled Analysis for Nearly Incompressible and Impermeable Saturated Porous Media on Mixed Finite Element Method: II. Verifications
,”
KSCE J. Civil Eng.
,
14
(
1
), pp.
17
24
.10.1007/s12205-010-0017-8
You do not currently have access to this content.