A review of the development of hybrid atomistic–continuum methods for dense fluids

Abstract

In recent years, there has been an increasing interest in simulating dynamical phenomena of multiscale systems. This was brought about in large part by the ever growing field of nanotechnology, in which nanodevices are often part of larger systems. Molecular Dynamics (MD) provides a valuable tool for modeling systems at the nanoscale. However, the atomistic modeling of macroscopic problems is still beyond the reach of current MD simulations due to their prohibitive computational requirements. The development of hybrid techniques that combine continuum and atomistic descriptions can alleviate such limitations. This can be accomplished by limiting the use of MD to regions where the atomistic scales need to be resolved, while using a continuum-based solver for the remainder of the domain. The computational savings of such a formulation will strongly depend on the relative size of the MD region to that of the continuum, and the extent of the overlap where information is exchanged between the two subdomains. Such methods are crucial for the proficient advancement and better understanding of nanodevices interacting with microscale systems. In this article, an account of the development of hybrid atomistic–continuum (HAC) models for dense flows is presented. The focus is on domain-decomposition-based HAC models. Here, the domain is divided into a relatively small region where atomistic details are important, and a larger region where the continuum description of the fluid is applicable. Of primary concern is how to accurately couple the atomistic and continuum domains, a challenge that manifests itself in the imposition of boundary conditions in an internally consistent manner. Two main approaches: state variable (Dirichlet), and flux-exchange schemes are analyzed and compared. A review of some applications utilizing such HAC models is also provided.

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Notes

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    In keeping with their original work, throughout the paper the atomistic–continuum interface will be referred to as HSI.

References

  1. Allen M, Tildesley D (1987) Computer simulation of liquids. Clarendon Press, Oxford

    Google Scholar 

  2. Baldini G, Cannone F, Chirico G (2005) Pre-unfolding resonant oscillations of single green fluorescent protein molecules. Science 309(5737):1096–1100

    Article  Google Scholar 

  3. Barrat J, Chiaruttini F (2003) Kapitza resistance at the liquid-solid interface. Mol Phys 101(11):1605–1610

    Article  Google Scholar 

  4. Barsky S, Delgado-Buscalioni R, Coveney PV (2004) Comparison of molecular dynamics with hybrid continuum-molecular dynamics for a single tethered polymer in a solvent. J Chem Phys 121(5):2403–2411

    Article  Google Scholar 

  5. Berendsen HJC, Postma JPM, Van Gunsteren WF, Dinola A, Haak JR (1984) Molecular dynamics with coupling to an external bath. J Chem Phys 81(8):3684–3690

    Article  Google Scholar 

  6. Borgelt P, Hoheisel C, Stell G (1990) Exact molecular dynamics and kinetic theory results for thermal transport coefficients of the Lennard-Jones Argon fluid in a wide region of states. Phys Rev A 42(2):789–794

    Article  Google Scholar 

  7. Brenner MP, Shi XD, Nagel SR (1994) Iterated instabilities during droplet fission. Phys Rev Lett 73(25):3391–3394

    Article  Google Scholar 

  8. Broughton JQ, Meli CA, Vashishta P, Kalia RK (1997) Direct atomistic simulation of quartz crystal oscillators: bulk properties and nanoscale devices. Phys Rev B 56(2):611–618

    Article  Google Scholar 

  9. Burt JM, Boyd ID (2009) A hybrid particle approach for continuum and rarefied flow simulation. J Comput Phys 228(2):460–475

    MATH  Article  Google Scholar 

  10. Chatterji A, Horbach J (2005) Combining molecular dynamics with Lattice Boltzmann: a hybrid method for the simulation of (charged) colloidal systems. J Chem Phys 122(18):1–12

    Article  Google Scholar 

  11. Cui J, He G, Qi D (2006) A constrained particle dynamics for continuum-particle hybrid method in micro- and nano-fluidics. Acta Mech Sin 26(6):503–508

    Article  Google Scholar 

  12. De Fabritiis G, Delgado-Buscalioni R, Coveney PV (2004) Energy controlled insertion of polar molecules in dense fluids. J Chem Phys 121(24):12139–12142

    Article  Google Scholar 

  13. De Fabritiis G, Delgado-Buscalioni R, Coveney PV (2006) Multiscale modeling of liquids with molecular specificity. Phys Rev Lett 97(13):134501

    Article  Google Scholar 

  14. Delgado-Buscalioni R, Coveney PV (2003) Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow. Phys Rev E 67(4):046704

    Article  Google Scholar 

  15. Delgado-Buscalioni R, Coveney PV (2003) USHER: an algorithm for particle insertion in dense fluids. J Chem Phys 119(2):978–987

    Article  Google Scholar 

  16. Delgado-Buscalioni R, Coveney PV (2004) Hybrid molecular-continuum fluid dynamics. Philos Trans R Soc Lond A 362(1821):1639–1654

    Article  MathSciNet  Google Scholar 

  17. Delgado-Buscalioni R, De Fabritiis D (2007) Embedding molecular dynamics within fluctuating hydrodynamics in multiscale simulations of liquids. Phys Rev E 76(3):036709

    Article  Google Scholar 

  18. Delgado-Buscalioni R, Flekkoy EG, Coveney PV (2005) Fluctuations and continuity in particle-continuum hybrid simulations of unsteady flows based on flux-exchange. Europhys Lett 69(6):959–965

    Article  Google Scholar 

  19. Delgado-Buscalioni R, Coveney PV, De Fabritiis G (2008) Towards multi-scale modelling of complex liquids using hybrid particle-continuum schemes. Proc Inst Mech Eng C 222(5):769–776

    Article  Google Scholar 

  20. Delgado-Buscalioni R, Kremer K, Praprotnik M (2008) Concurrent triple-scale simulation of molecular liquids. J Chem Phys 128(11):114110

    Article  Google Scholar 

  21. Doyle PS, Ladoux B, Viovy JL (2000) Dynamics of a tethered polymer in shear flow. Phys Rev Lett 84(20):4769–4772

    Article  Google Scholar 

  22. Dupuis A, Kotsalis EM, Koumoutsakos P (2007) Coupling Lattice Boltzmann and molecular dynamics models for dense fluids. Phys Rev E 75(4):046704

    Article  Google Scholar 

  23. Espanol P, Revenga M (2003) Smoothed dissipative particle dynamics. Phys Rev E 67(2):026705

    Article  Google Scholar 

  24. Evans DJ, Morriss GP (2007) Statistical mechanics of nonequilibrium liquids. ANU E Press, Australia

    Google Scholar 

  25. Fedosov DA, Karniadakis GE (2009) Triple-Decker: interfacing atomistic-mesoscopic-continuum flow regimes. J Comput Phys 228(4):1157–1171

    MATH  Article  MathSciNet  Google Scholar 

  26. Flekkoy EG, Wagner G, Feder J (2000) Hybrid model for combined particle and continuum dynamics. Europhys Lett 52(3):271–276

    Article  Google Scholar 

  27. Flekkoy EG, Delgado-Buscalioni R, Coveney PV (2005) Flux boundary conditions in particle simulations. Phys Rev E 72(2):1–9

    Article  Google Scholar 

  28. Frenkel D, Smith B (1996) Understanding molecular simulations. Academic Press, London

    Google Scholar 

  29. Fyta M, Kaxiras E, Melchionna S, Succi S (2008) Multiscale simulation of nanobiological flows. Comput Sci Eng 10(4):10–19

    Article  Google Scholar 

  30. Garcia AL, Bell JB, Crutchfield WY, Aldery BJ (1999) Adaptive mesh and algorithm refinement using direct simulation Monte Carlo. J Comput Phys 154:134–155

    MATH  Article  Google Scholar 

  31. Grest GS, Kremer K (1986) Molecular dynamics simulation for polymers in the presence of a heat bath. Phys Rev A 33(5):3628–3631

    Article  Google Scholar 

  32. Guo Z, Zheng C, Shi B (2002) Discrete lattice effects on the forcing term in the Lattice Boltzmann method. Phys Rev E 65(4):046308

    Article  MathSciNet  Google Scholar 

  33. Hadjiconstantinou NG (1999) Hybrid atomistic-continuum formulations and the moving contact-line problem. J Comput Phys 154:245–265

    MATH  Article  Google Scholar 

  34. Hadjiconstantinou NG (2005) Discussion of recent developments in hybrid atomistic-continuum methods for multiscale hydrodynamics. Bull Pol Acad Sci Tech Sci 53(4):335–342

    Google Scholar 

  35. Hadjiconstantinou NG, Patera AT (1997) Heterogeneous atomistic-continuum representations for dense fluid systems. Int J Mod Phys 8(4):967–976

    Article  Google Scholar 

  36. Hadjiconstantinou NG, Garcia AL, Bazant MZ, He G (2003) Statistical error in particle simulations of hydrodynamic phenomena. J Comput Phys 187(1):274–297

    MATH  Article  MathSciNet  Google Scholar 

  37. Hansen JP, McDonald IR (1986) Theory of simple liquids. Academic Press, London

    Google Scholar 

  38. Hash DB, Hassan HA (1995) A hybrid DSMC/Navier-Stokes solver. AIAA Paper 95-0414

  39. Heyes DM (1988) Simple expressions for the self-diffusion coefficient, shear viscosity and thermal conductivity of Lennard-Jones fluids. Chem Phys Lett 153(4):319–321

    Article  Google Scholar 

  40. Ho CM, Tai YC (1998) Micro-electro-mechanical-systems (MEMS) and fluid flows. Annu Rev Fluid Mech 30:579–612

    Article  Google Scholar 

  41. Hoover WG, De Groot AJ, Hoover CG (1992) Massively parallel computer simulation of plane-strain elastic-plastic flow via nonequilibrium molecular dynamics and Lagrangian continuum mechanics. Comput Phys 6(2):155–167

    Article  Google Scholar 

  42. Hu G, Li D (2007) Multiscale phenomena in microfluidics and nanofluidics. Chem Eng Sci 62(13):3443–3454

    Article  Google Scholar 

  43. Johnson JK, Zollweg JA, Gubbins KE (1993) The Lennard-Jones equation of state revisited. Mol Phys 78(3):591–618

    Article  Google Scholar 

  44. Kalweit M, Drikakis D (2008) Multiscale methods for micro/nano flows and materials. J Comput Theor Nanosci 5(9):1923–1938

    Article  Google Scholar 

  45. Kalweit M, Drikakis D (2008) Coupling strategies for hybrid molecular-continuum simulation methods. Proc Inst Mech Eng C 222(5):797–806

    Google Scholar 

  46. Karniadakis G, Beskok A, Aluru N (2005) Microflows and nanoflows, fundamentals and simulation. Springer, New York

    Google Scholar 

  47. Kevrekidis IG, Gear CW, Hyman JM, Panagiotis GK, Runborg O, Theodoropoulos C (2003) Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis. Commun Math Sci 1(4):715–762

    MATH  MathSciNet  Google Scholar 

  48. Kevrekidis IG, Gear CW, Hummer G (2004) Equation-free: the computer-aided analysis of complex multiscale systems. AIChE J 50(7):1346–1355

    Article  Google Scholar 

  49. Kohlhoff S, Gumbsch P, Fischmeister HF (1991) Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model. Philos Mag A 64(4):851–878

    Article  Google Scholar 

  50. Koplik J, Banavar JR (1995) Continuum deductions from molecular hydrodynamics. Annu Rev Fluid Mech 27(1):257–292

    Article  Google Scholar 

  51. Koplik J, Banavar JR (1995) Corner flow in the sliding plate problem. Phys Fluids 7(12):3118–3125

    MATH  Article  Google Scholar 

  52. Kotsalis EM, Walther JH, Koumoutsakos P (2007) Control of density fluctuations in atomistic-continuum simulations of dense liquids. Phys Rev E 76(1):016709

    Article  Google Scholar 

  53. Kotsalis EM, Walther JH, Kaxiras E, Koumoutsakos P (2009) Control algorithm for multiscale flow simulations of water. Phys Rev E 79(4):045701

    Article  Google Scholar 

  54. Koumoutsakos P (2005) Multiscale flow simulations using particles. Annu Rev Fluid Mech 37:457–487

    Article  MathSciNet  Google Scholar 

  55. Kunugi T, Muko K, Shibahara M (2004) Ultrahigh heat transfer enhancement using nano-porous layer. Superlattices Microstruct 35(3–6):531–542

    Article  Google Scholar 

  56. Landau LD, Lifshitz EM (1959) Fluid mechanics. Pergamon Press, New York

    Google Scholar 

  57. LeDuc P, Haber C, Bao G, Wirtz D (1999) Dynamics of individual flexible polymers in a shear flow. Nature 399(6736):564–566

    Article  Google Scholar 

  58. Li J, Liao D, Yip S (1998) Coupling continuum to molecular-dynamics simulation: reflecting particle method and the field estimator. Phys Rev E 57(6):7259–7267

    Article  Google Scholar 

  59. Li J, Liao D, Yip S (1999) Nearly exact solution for coupled continuum/MD fluid simulation. J Comput Aided Mater Des 6(2):95–102

    Article  Google Scholar 

  60. Li J, Liao D, Yip S (1999) Imposing field boundary conditions in md simulation of fluids: optimal particle controller and buffer zone feedback. Mater Res Soc Symp Proc 538:473–478

    Google Scholar 

  61. Lions PL (1988) On the Schwarz alternating method. In: Glowinski R (ed) First international symposium on domain decomposition methods for partial differential equations. SIAM, Philadelphia, USA, pp 1–42

    Google Scholar 

  62. Liu J, Chen S, Nie X, Robbins MO (2007) A continuum-atomistic simulation of heat transfer in micro- and nano-flows. J Comput Phys 227(1):279–291

    MATH  Article  Google Scholar 

  63. Liu J, Chen S, Nie X, Robbins MO (2008) A continuum-atomistic multi-timescale algorithm for micro/nano flows. Commun Comput Phys 4(5):1279–1291

    Google Scholar 

  64. Macpherson GB, Reese JM (2008) Molecular dynamics in arbitrary geometries: parallel evaluation of pair forces. Mol Simul 34(1):97–115

    Article  Google Scholar 

  65. Maday Y, Patera AT (1989) Spectral element methods for the incompressible Navier-Stokes equations. In: Noor AK, Oden JT (ed) State-of-the-art surveys in computational mechanics. ASME, New York, USA, pp 71–143

    Google Scholar 

  66. McCormick SF (1989) Multilevel adaptive methods for partial differential equations. SIAM, Philadelphia

    Google Scholar 

  67. Mukhopadhyay S, Abraham J (2009) A particle-based multiscale model for submicron fluid flows. Phys Fluids 21(2):027102

    Article  Google Scholar 

  68. Nie XB, Chen SY, E WN, Robbins MO (2004) A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. J Fluid Mech 500:55–64

    MATH  Article  Google Scholar 

  69. Nie X, Chen S, Robbins MO (2004) Hybrid continuum-atomistic simulation of singular corner flow. Phys Fluids 16(10):3579–3591

    Article  Google Scholar 

  70. Nie X, Robbins MO, Chen S (2006) Resolving singular forces in cavity flow: multiscale modeling from atomic to millimeter scales. Phys Rev Lett 96(13):134501

    Article  Google Scholar 

  71. O’Connell ST, Thompson PA (1995) Molecular dynamics-continuum hybrid computations: a tool for studying complex fluid flows. Phys Rev E 52(6):R5792–R5795

    Article  Google Scholar 

  72. Patera AT (1984) A spectral element method for fluid dynamics—laminar flow in a channel expansion. J Comput Phys 54(3):468–488

    MATH  Article  MathSciNet  Google Scholar 

  73. Pivkin IV, Karniadakis GE (2006) Controlling density fluctuations in wall-bounded dissipative particle dynamics systems. Phys Rev Lett 96(20):206001

    Article  Google Scholar 

  74. Praprotnik K, Delle Site L, Kremer K (2005) Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly. J Chem Phys 123(22):1–14

    Article  Google Scholar 

  75. Praprotnik K, Delle Site L, Kremer K (2006) Adaptive resolution scheme for efficient hybrid atomistic-mesoscale molecular dynamics simulations of dense liquids. Phys Rev E 73(6):066701

    Article  Google Scholar 

  76. Praprotnik M, Site LD, Kremer K (2008) Multiscale simulation of soft matter: from scale bridging to adaptive resolution. Annu Rev Phys Chem 59:545–571

    Article  Google Scholar 

  77. Ren W (2007) Analytical and numerical study of coupled atomistic-continuum methods for fluids. J Comput Phys 227(2):1353–1371

    MATH  Article  MathSciNet  Google Scholar 

  78. Ren W, Weinan E (2005) Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. J Comput Phys 204(1):1–26

    MATH  Article  MathSciNet  Google Scholar 

  79. Saletan EJ, Cromer AH (1971) Theoretical mechanics. Wiley, New York

  80. Schmatko T, Hervet H, Leger L (2005) Friction and slip at simple fluid-solid interfaces: the roles of the molecular shape and the solid-liquid interaction. Phys Rev Lett 94(24):1–4

    Article  Google Scholar 

  81. Schoch RB, Han J, Renaud P (2008) Transport phenomena in nanofluidics. Rev Mod Phys 80(3):839–883

    Article  Google Scholar 

  82. Schubert K, Brandner J, Fichtner M, Linder G, Schygulla U, Wenka A (2001) Microstructure devices for applications in thermal and chemical process engineering. Microscale Thermophys Eng 5(1):17–39

    Article  Google Scholar 

  83. Schwartzentruber TE, Scalabrin LC, Boyd ID (2007) A modular particle-continuum numerical method for hypersonic non-equilibrium gas flows. J Comput Phys 225(1):1159–1174

    MATH  Article  MathSciNet  Google Scholar 

  84. Slater GW, Holm C, Chubynsky MV, de Haan HW, Dubé A, Grass K, Hickey OA, Kingsburry C, Sean D, Shendruk TN, Zhan L (2009) Modeling the separation of macromolecules: a review of current computer simulation methods. Electrophoresis 30(5):792–818

    Article  Google Scholar 

  85. Stroock AD, Dertinger SKW, Ajdari A, Mezic I, Stone HA, Whitesides GM (2002) Chaotic mixer for microchannels. Science 295(5555):647–651

    Article  Google Scholar 

  86. Succi S (2001) The Lattice Boltzmann equation, for fluid dynamics and beyond. Oxford University Press, Oxford

    Google Scholar 

  87. Succi S, Filippova O, Smith G, Kaxiras E (2001) Applying the Lattice Boltzmann equation to multiscale fluid problems. Comput Sci Eng 3(6):26–37

    Article  Google Scholar 

  88. Sun Q, Boyd ID, Candler GV (2004) A hybrid continuum/particle approach for modeling subsonic, rarefied gas flows. J Comput Phys 194(1):256–277

    MATH  Article  Google Scholar 

  89. Sun J, He Y, Tao W (2009) Molecular dynamics-continuum hybrid simulation for condensation of gas flow in a microchannel. Microfluid Nanofluid 7(3):407–422

    Google Scholar 

  90. Thompson PA, Robbins MO (1989) Simulations of contact-line motion: slip and the dynamic contact angle. Phys Rev Lett 63(7):766–769

    Article  Google Scholar 

  91. Thompson PA, Robbins MO (1990) Origin of stick-slip motion in boundary lubrication. Science 250(4982):792–794

    Article  Google Scholar 

  92. Thompson PA, Brickerhoff WB, Robbins MO (1993) Microscopic studies of static and dynamic contact angles. J Adhes Sci Technol 7(6):535–554

    Article  Google Scholar 

  93. Wadsworth DC, Erwin DA (1990) One-dimensional hybrid continuum/particle simulation approach for rarefied hypersonic flows. AIAA Paper 90-1690

  94. Wagner G, Flekkoy EG (2004) Hybrid computations with flux exchange. Philos Trans R Soc Lond A 362(1821):1655–1665

    Article  MathSciNet  Google Scholar 

  95. Wagner G, Flekkoy E, Feder J, Jossang T (2002) Coupling molecular dynamics and continuum dynamics. Comput Phys Commun 147(1–2):670–673

    MATH  Article  Google Scholar 

  96. Wang Y, He G (2007) A dynamic coupling model for hybrid atomistic-continuum computations. Chem Eng Sci 62(13):3574–3579

    Article  MathSciNet  Google Scholar 

  97. Weinan E, Engquist B, Li X, Ren W, Vanden-Eijnden E (2007) Heterogeneous multiscale methods: a review. Commun Comput Phys 2(3):367–450

    MATH  MathSciNet  Google Scholar 

  98. Werder T, Walther JH, Koumoutsakos P (2005) Hybrid atomistic-continuum method for the simulation of dense fluid flows. J Comput Phys 205(1):373–390

    MATH  Article  MathSciNet  Google Scholar 

  99. Wijesinghe HS, Hadjiconstantinou NG (2004) Discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics. Int J Multiscale Comput Eng 2(2):189–202

    Article  Google Scholar 

  100. Wolf-Gladrow DA (2005) Lattice-gas cellular automata and Lattice Boltzmann models—an introduction. Springer, New York

    Google Scholar 

  101. Yasuda S, Yamamoto R (2008) A model for hybrid simulations of molecular dynamics and computational fluid dynamics. Phys Fluids 20(11):113101

    Article  Google Scholar 

  102. Yen TH, Soong CY, Tzeng PY (2007) Hybrid molecular dynamics-continuum simulation for nano/mesoscale channel flows. Microfluid Nanofluid 3(6):665–675

    Article  Google Scholar 

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Mohamed, K.M., Mohamad, A.A. A review of the development of hybrid atomistic–continuum methods for dense fluids. Microfluid Nanofluid 8, 283–302 (2010). https://doi.org/10.1007/s10404-009-0529-z

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Keywords

  • Hybrid atomistic–continuum
  • Coupling
  • Molecular dynamics
  • Multiscale
  • Dense fluids
  • Microfluidics
  • Nanofluidics