The particle-continuum hybrid Laplacian method is extended as a framework for modeling all transport phenomena in fluids at the micro and nanoscale including multicomponent mass transfer and chemical reactions. The method is explained, and the micro-to-macro and macro-to-micro coupling steps are discussed. Two techniques for noise reduction (namely, the bonsai box (BB) and the seamless strategy) are discussed. Comparisons with benchmark full-molecular dynamics (MD) cases for micro and nano thermal and reacting flows show excellent agreement and good computational efficiency.

References

References
1.
Jaworski
,
Z.
, and
Zakrzewska
,
B.
,
2011
, “
Towards Multiscale Modeling in Product Engineering
,”
Comput. Chem. Eng.
,
35
(
3
), pp.
434
445
.10.1016/j.compchemeng.2010.05.009
2.
Gad-El-Hak
,
M.
,
2006
,
MEMS: Introduction and Fundamentals
,
Taylor & Francis
, Boca Raton, FL
3.
Chen
,
D. T. N.
,
Wen
,
Q.
,
Janmey
,
P. A.
,
Crocker
,
J. C.
, and
Yodh
,
A. G.
,
2010
, “
Rheology of soft materials
,”
Annu. Rev. Condens. Matter Phys.
,
1
, pp.
301
322
.10.1146/annurev-conmatphys-070909-104120
4.
O'Connell
,
S. T.
, and
Thompson
,
T. A.
,
1995
, “
Molecular Dynamics-Continuum Hybrid Computations: A Tool for Studying Complex Fluid Flows
,”
Phys. Rev. E
,
52
, pp.
5792
5795
.10.1103/PhysRevE.52.R5792
5.
Mohamed
,
K. M.
, and
Mohamad
,
A. A.
,
2010
, “
A Review of the Development of Hybrid Atomistic-Continuum Methods for Dense Fluids
,”
Microfluid. Nanofluid.
,
8
(
3
), pp.
283
302
.10.1007/s10404-009-0529-z
6.
Li
,
J.
,
Liao
,
D.
, and
Yip
,
S.
,
1998
, “
Coupling Continuum to Molecular-Dynamics Simulation: Reflecting Particle Method and the Field Estimator
,”
Phys. Rev. E
,
57
(
6
), pp.
7259
7267
.10.1103/PhysRevE.57.7259
7.
Hadjiconstantinou
,
N. G.
, and
Patera
,
A. T.
,
1997
, “
Heterogeneous Atomistic-Continuum Representations for Dense Fluid Systems
,”
Int. J. Mod. Phys. C
,
8
(
4
), pp.
967
976
.10.1142/S0129183197000837
8.
Nie
,
X.
,
Chen
,
S. Y.
,
E
,
W. N.
, and
Robbins
,
M. O.
,
2004
, “
A Continuum and Molecular Dynamics Hybrid Method for Micro- and Nano-Fluid Flow
,”
J. Fluid Mech.
,
500
, pp.
55
64
10.1017/S0022112003007225
9.
Delgado-Buscalioni
,
R.
, and
Coveney
,
P. V.
,
2004
, “
Hybrid Molecular-Continuum Fluid Dynamics
,”
Philos. Trans. R. Soc. London, Ser. A
,
362
(
1821
), pp.
1639
1654
.10.1098/rsta.2005.1623
10.
Koumoutsakos
,
P.
,
2005
, “
Multiscale Flow Simulations Using Particles
,”
Annu. Rev. Fluid Mech.
,
37
, pp.
457
487
.10.1146/annurev.fluid.37.061903.175753
11.
Ren
,
W.
, and
E
,
W.
,
2005
, “
Heterogeneous Multiscale Method for the Modelling of Complex Fluids and Micro-Fluidics
,”
J. Comput. Phys.
,
204
(1), pp.
1
26
.10.1016/j.jcp.2004.10.001
12.
Asproulis
,
N.
,
Kalweit
,
M.
, and
Drikakis
,
D.
,
2012
, “
A Hybrid Molecular Continuum Method Using Point Wise Coupling
,”
Adv. Eng. Software
,
46
(
1
), pp.
85
92
.10.1016/j.advengsoft.2010.10.010
13.
Borg
,
M. K.
,
Lockerby
,
D. A.
, and
Reese
,
J. M.
,
2013
, “
A Multiscale Method for Micro/Nano Flows of High Aspect Ratio
,”
J. Comput. Phys.
,
233
, pp.
400
413
.10.1016/j.jcp.2012.09.009
14.
Liu
,
J.
,
Chen
,
S.
,
Nie
,
X.
, and
Robbins
,
M. O.
,
2007
, “
A Continuum-Atomistic Simulation of Heat Transfer in Micro- and Nano-Flows
,”
J. Comput. Phys.
,
227
(
1
), pp.
279
291
.10.1016/j.jcp.2007.07.014
15.
Alexiadis
,
A.
,
Lockerby
,
D. A.
,
Borg
,
M. K.
, and
Reese
,
J. M.
,
2013
, “
A Laplacian-Based Algorithm for Non-Isothermal Atomistic-Continuum Hybrid Simulation of Micro and Nano-Flows
,”
Comput. Methods Appl. Mech. Eng.
,
264
, pp.
81
94
.10.1016/j.cma.2013.05.020
16.
Lo
,
C.
, and
Palmer
,
B.
,
1995
, “
Alternative Hamiltonian for Molecular Dynamics Simulations in the Grand Canonical Ensemble
,”
J. Chem. Phys.
,
102
(
2
), pp.
925
931
.10.1063/1.469159
17.
Shroll
,
R. M.
,
1999
, “
Molecular Dynamics Simulations in the Grand Canonical Ensemble: Formulation of a Bias Potential for Umbrella Sampling
,”
J. Chem. Phys.
,
110
(
17
), pp.
8295
8302
.10.1063/1.478791
18.
Lupkowski
,
M.
, and
Van Swol
,
F.
,
1991
, “
Ultrathin Films Under Shear
,”
J. Chem. Phys.
,
95
(3), pp.
1995
1998
.10.1063/1.460997
19.
Papadopoulou
,
A.
,
Becker
,
E. D.
,
Lupkowski
,
M.
, and
Van Swol
,
F.
,
1993
, “
Molecular Dynamics and Monte Carlo Simulations in the Grand Canonical Ensemble: Local Versus Global Control
,”
J. Chem. Phys.
,
98
(
6
), pp.
4897
4908
.10.1063/1.464945
20.
Heffelfinger
,
G. S.
, and
Van Swol
,
F.
,
1994
, “
Diffusion in Lennard-Jones Fluids Using Dual Control Volume Grand Canonical Molecular Dynamics Simulation (DCV-GCMD)
,”
J. Chem. Phys.
,
100
(
10
), pp.
7548
7552
.10.1063/1.466849
21.
Boinepalli
,
S.
, and
Attard
,
P.
,
2003
, “
Grand Canonical Molecular Dynamics
,”
J. Chem. Phys.
,
119
(
24
), pp.
12769
12775
.10.1063/1.1629079
22.
Drikakis
,
D.
, and
Asproulis
,
N.
,
2010
, “
Multi-Scale Computational Modelling of Flow and Heat Transfer
,”
Int. J. Numer. Methods Heat Fluid Flow
,
20
(
5
), pp.
517
528
.10.1108/09615531011048222
23.
E
,
W.
,
Ren
,
W.
, and
Vanden-Eijnden
,
E.
,
2009
, “
A General Strategy for Designing Seamless Multiscale Methods
,”
J. Comput. Phys.
,
228
(
15
), pp.
5437
5453
.10.1016/j.jcp.2009.04.030
24.
Trozzi
,
C.
, and
Ciccotti
,
G.
,
1984
, “
Stationary Non-Equilibrium States by Molecular Dynamics. II. Newton's Law
,”
Phys. Rev. A
,
29
(
2
), pp.
916
925
.10.1103/PhysRevA.29.916
25.
Alexiadis
,
A.
,
Lockerby
,
D. A.
,
Borg
,
M. K.
, and
Reese
,
J. M.
,
2014
, “
The Atomistic-Continuum Hybrid Taxonomy and the Hybrid-Hybrid Approach
,”
Int. J. Numer. Methods Eng.
,
98
(
7
), pp.
534
546
.10.1002/nme.4646
26.
Gillespie
,
D.
,
1976
, “
A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions
,”
J. Comput. Phys.
,
22
(
4
), pp.
403
434
.10.1016/0021-9991(76)90041-3
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