Lattice Boltzmann methods for thermal flows: Continuum limit and applications to compressible Rayleigh-Taylor systems

Physics of Fluids

Volumn 22, Issue 5, 2010, Pages 1-21

  Scagliarini, A ^a   Biferale, L ^a   Sbragaglia, M ^a   Sugiyama, K ^b   Toschi, F ^c  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITY OF TOKYO   (Japan)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; FINITE DIFFERENCE METHOD; INTEGRAL EQUATIONS; KINETIC THEORY; MIXING;

ASYMMETRIC GROWTHS; BULK TEMPERATURES; FINITE DIFFERENCE SCHEME; LATTICE BOLTZMANN METHOD; NUMERICAL ALGORITHMS; RAYLEIGH-TAYLOR INSTABILITIES; STRATIFIED FLOWS; TEMPERATURE JUMP;

NAVIER STOKES EQUATIONS;

EID: 77955618379     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3392774     Document Type: Article

References (74)

1. Shan X. Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 1993, 47:1815. PLEEE8, 1063-651X, 10.1103/PhysRevE.47.1815
2. Swift M.R. Osborn W.R. Yeomans J.M. Lattice Boltzmann simulation of nonideal fluids. Phys. Rev. Lett. 1995, 75:830. PRLTAO, 0031-9007, 10.1103/PhysRevLett.75.830
3. Li Q. Wagner A.J. Symmetric free-energy-based multicomponent lattice Boltzmann method. Phys. Rev. E 2007, 76:036701. PLEEE8, 1063-651X, 10.1103/PhysRevE.76.036701
4. He X. Luo L.S. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 1997, 56:6811. PLEEE8, 1063-651X, 10.1103/PhysRevE.56.6811
5. Ladd A.J. C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. 2. Numerical results. J. Fluid Mech. 1994, 271:311. JFLSA7, 0022-1120, 10.1017/S0022112094001783
6. Harting J. Kunert C. Hyvaluoma J. Lattice Boltzmann simulations in microfluidics: Probing the no-slip boundary condition in hydrophobic, rough, and surface nanobubble laden microchannels. Microfluid. Nanofluid. 2010, 8:1. MNIAAR, 1613-4982, 10.1007/s10404-009-0506-6
7. Duenweg B. Ladd A.J. C. Lattice Boltzmann simulations of soft matter systems. Adv. Polym. Sci. 2009, 221:89. APSIDK, 0065-3195
8. Nourgaliev R.R. Dinh T.N. Theofanous T.G. Joseph D. The Lattice Boltzmann equation method: Theoretical interpretation, numerics and implications. Int. J. Multiphase Flow 2003, 29:117. IJMFBP, 0301-9322, 10.1016/S0301-9322(02)00108-8
9. Wolf-Gladrow D. Lattice-Gas Cellular Automata And Lattice Boltzmann Models 2000, (Springer, New York)
10. Benzi R. Succi S. Vergassola M. The lattice Boltzmann equation: Theory and applications. Phys. Rep. 1992, 222:145. PRPLCM, 0370-1573, 10.1016/0370-1573(92)90090-M
11. Chen S. Doolen G. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 1998, 30:329. ARVFA3, 0066-4189, 10.1146/annurev.fluid.30.1.329
12. Bathnagar P.-.L. Gross E. Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 1954, 94:511. PRVAAH, 0096-8250, 10.1103/PhysRev.94.511
13. Shan X. He X. Discretization of the velocity space in the solution of the Boltzmann equation. Phys. Rev. Lett. 1998, 80:65. PRLTAO, 0031-9007, 10.1103/PhysRevLett.80.65
14. Martys N.S. Shan X. Chen H. Evaluation of the extrenal force term in the discrete Boltzmann equation. Phys. Rev. E 1998, 58:6855. PLEEE8, 1063-651X, 10.1103/PhysRevE.58.6855
15. Shan X. Yuan F. Chen H. Kinetic theory representation of hydrodynamics: A way beyond the Navier-Stokes equation. J. Fluid Mech. 2006, 550:413. JFLSA7, 0022-1120, 10.1017/S0022112005008153
16. He X. Doolen G. Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows. J. Stat. Phys. 2002, 107:309. JSTPBS, 0022-4715, 10.1023/A:1014527108336
17. Benzi R. Biferale L. Sbragaglia M. Succi S. Toschi F. Mesoscopic modelling of a two-phase flow in presence of the boundaries: The contact angle. Phys. Rev. E 2006, 74:021509. PLEEE8, 1063-651X, 10.1103/PhysRevE.74.021509
18. Sbragaglia M. Benzi R. Biferale L. Succi S. Toschi F. Surface roughness-hydrophobicity coupling in microchannel and nanochannel flows. Phys. Rev. Lett. 2006, 97:204503. PRLTAO, 0031-9007, 10.1103/PhysRevLett.97.204503
19. Hyvaluoma J. Harting J. Slip flow over structured surfaces with entrapped microbubbles. Phys. Rev. Lett. 2008, 100:246001. PRLTAO, 0031-9007, 10.1103/PhysRevLett.100.246001
20. Lallemand P. Luo L.S. Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions. Phys. Rev. E 2003, 68:036706. PLEEE8, 1063-651X, 10.1103/PhysRevE.68.036706
21. Prasianakis N.I. Karlin I.V. Mantzaras J. Boulouchos K.B. Lattice Boltzmann method with restored Galilean invariance. Phys. Rev. E 2009, 79:066702. PLEEE8, 1063-651X, 10.1103/PhysRevE.79.066702
22. Prasianakis N.I. Karlin I.V. Lattice Boltzmann method for thermal flow simulation on standard lattices. Phys. Rev. E 2007, 76:016702. PLEEE8, 1063-651X, 10.1103/PhysRevE.76.016702
23. Sofonea V. Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters. J. Comput. Phys. 2009, 228:6107. JCTPAH, 0021-9991, 10.1016/j.jcp.2009.05.009
24. Gonnella G. Lamura A. Sofonea V. Lattice Boltzmann simulation of thermal nonideal fluids. Phys. Rev. E 2007, 76:036703. PLEEE8, 1063-651X, 10.1103/PhysRevE.76.036703
25. Watari M. Velocity slip and temperature jump simulations by the three-dimensional thermal finite-difference lattice Boltzmann method. Phys. Rev. E 2009, 79:066706. PLEEE8, 1063-651X, 10.1103/PhysRevE.79.066706
26. Philippi P.C. Hegele L.A. dos Santos L.O. E. Surmas R. From the continuous to the lattice Boltzmann equation: The discretization problem and thermal models. Phys. Rev. E 2006, 73:056702. PLEEE8, 1063-651X, 10.1103/PhysRevE.73.056702
27. Nie X. Shan X. Chen H. Thermal lattice Boltzmann model for gases with internal degrees of freedom. Phys. Rev. E 2008, 77:035701. PLEEE8, 1063-651X, 10.1103/PhysRevE.77.035701.
28. Shan X. Chen H. A general multi-relaxation-time Boltzmann collision model. Int. J. Mod. Phys. C 2007, 18:635. IJMPEO, 0129-1831, 10.1142/S0129183107010887
29. Surmas R. Pico Ortiz C.E. Philippi P.C. Simulating thermohydrodynamics by finite difference solutions of the Boltzmann equations. Eur. Phys. J. Spec. Top. 2009, 171:81. ZZZZZZ, 1951-6355, 10.1140/epjst/e2009-01014-x
30. Ansumali S. Karlin I. Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E 2002, 66:026311. PLEEE8, 1063-651X, 10.1103/PhysRevE.66.026311
31. Siebert D.N. Hegele L.A. Philippi P.C. Lattice Boltzmann equation linear stability analysis: Thermal and athermal models. Phys. Rev. E 2008, 77:026707. PLEEE8, 1063-651X, 10.1103/PhysRevE.77.026707
32. Sbragaglia M. Benzi R. Biferale L. Chen H. Shan X. Succi S. Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria. J. Fluid Mech. 2009, 628:299. JFLSA7, 0022-1120, 10.1017/S002211200900665X
33. Spiegel E.A. Convective instability in a compressible atmosphere. Astrophys. J. 1965, 141:1068. ASJOAB, 0004-637X, 10.1086/148197
34. Spiegel E.A. Veronis G. On the Boussinesq approximation for a compressible fluid. Astrophys. J. 1960, 131:442. ASJOAB, 0004-637X, 10.1086/146849
35. Ahlers G. Grossmann S. Lohse D. Heat transfer and large-scale dynamics in turbulent Rayleigh-Benard convection. Rev. Mod. Phys. 2009, 81:503. RMPHAT, 0034-6861, 10.1103/RevModPhys.81.503
36. Buick J.M. Greated C.A. Gravity in a lattice Boltzmann model. Phys. Rev. E 2000, 61:5307. PLEEE8, 1063-651X, 10.1103/PhysRevE.61.5307
37. Guo Z. Zheng C. Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 2002, 65:046308. PLEEE8, 1063-651X, 10.1103/PhysRevE.65.046308
38. Celani A. Mazzino A. Muratore-Ginanneschi P. Vozella L. Phase-field model for the Rayleigh-Taylor instability of immiscible fluids. J. Fluid Mech. 2009, 622:115. JFLSA7, 0022-1120, 10.1017/S0022112008005120
39. Siebert D.N. Hegele L.A. Surmas R. Emerich Dos Santos L.O. Philippi P.C. Thermal lattice Boltzmann in two dimensions. Int. J. Mod. Phys. C 2007, 18:546. IJMPEO, 0129-1831, 10.1142/S0129183107010784
40. Frolich J. Gauthier S. Numerical investigations from compressible to isobaric Rayleigh-Benard convection in two dimensions. Eur. J. Mech. B/Fluids 1993, 12:141. EJBFEV, 0997-7546
41. Robinson F. Chan K. Non-Boussinesq simulations of Rayleigh-Benard convection in a perfect gas. Phys. Fluids 2004, 16:1321. PHFLE6, 1070-6631, 10.1063/1.1689350
42. T(H)ρ).
43. Landau L.D. Lifshitz E.M. Fluid Mechanics 1959, and, (Pergamon, London, ).
44. Thomas J. Weiss N. Tobias S. Downward pumping of magnetic flux as the cause of filamentary structures in sunspot penumbrae. Nature (London) 2002, 420:390. NATUAS, 0028-0836, 10.1038/nature01174
45. Brummell N.H. Turbulent compressible convection with rotation. Proceedings of the International Astronomical Union 2006, 2:417. 10.1017/S174392130700083X
46. Ahlers G. Araujo F.F. Funfschilling D. Grossmann S. Lohse D. Non-Oberbeck-Boussinesq effects in gaseous Rayleigh-Benard convection. Phys. Rev. Lett. 2007, 98:054501. PRLTAO, 0031-9007, 10.1103/PhysRevLett.98.054501
47. Ahlers G. Dressel B. Oh J. Pesch W. Strong non-Boussinesq effects near the onset of convection in a fluid near its critical point. J. Fluid Mech. 2010, 642:15. JFLSA7, 0022-1120, 10.1017/S0022112009991686
48. Zhang J. Wu X.L. Xia K.-.Q. Density fluctuations in strongly stratified two-dimensional turbulence. Phys. Rev. Lett. 2005, 94:174503. PRLTAO, 0031-9007, 10.1103/PhysRevLett.94.174503
49. Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability 1961, (Clarendon, Oxford, ).
50. Gough D.O. Moore D.R. Spiegel E.A. Weiss N.O. Convective instability in a compressible atmosphere. II. Astrophys. J. 1976, 206:536. ASJOAB, 0004-637X, 10.1086/154409
51. Graham E. Numerical simulation of two-dimensional compressible convection. J. Fluid Mech. 1975, 70:689. JFLSA7, 0022-1120, 10.1017/S0022112075002297
52. Stevens R.J. A. M. Verzicco R. Lohse D. Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection. J. Fluid Mech. 2010, 643:495. JFLSA7, 0022-1120, 10.1017/S0022112009992461
53. Chen H. Teixeira C. Molvig K. Realization of fluid boundary conditions via discrete Boltzmann dynamics. Int. J. Mod. Phys. C 1998, 9:1281. IJMPEO, 0129-1831, 10.1142/S0129183198001151
54. Sugiyama K. Calzavarini E. Grossmann S. Lohse D. Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Bènard convection in glycerol. Europhys. Lett. 2007, 80:34002. EULEEJ, 0295-5075, 10.1209/0295-5075/80/34002
55. Sugiyama K. Calzavarini E. Grossmann S. Lohse D. Flow organization in two-dimensional non-Oberbeck-Boussinesq Rayleigh-Bénard convection in water. J. Fluid Mech. 2009, 637:105. JFLSA7, 0022-1120, 10.1017/S0022112009008027
56. Lindl J.D. Inertial Confinement Fusion 1998, (Springer-Verlag, New York, ).
57. Zingale M. Woosley S.E. Rendleman C.A. Day M.S. Bell J.B. Three-dimensional numerical simulations of Rayleigh-Taylor unstable flames in type Ia Supernovae. Astrophys. J. 2005, 632:1021. ASJOAB, 0004-637X, 10.1086/433164
58. Sharp D.H. An overview of Rayleigh-Taylor instability. Physica D 1984, 12:3. PDNPDT, 0167-2789, 10.1016/0167-2789(84)90510-4
59. Dimonte G. Youngs D.L. Dimits A. Weber S. Marinak M. Wunsch S. Garasi C. Robinson A. Andrews M.J. Ramaprabhu P. Calder A.C. Fryxell B. Biello J. Dursi L. MacNeice P. Olson K. Ricker P. Rosner R. Timmes F. Tufo H. Young Y.-.N. Zingale M. A comparative study of the Rayleigh-Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha group collaboration. Phys. Fluids 2004, 16:1668. PHFLE6, 1070-6631, 10.1063/1.1688328
60. Livescu D. Ristorcelli J.R. Gore R.A. Dean S.H. Cabot W.H. Cook A.W. High-Reynolds number Rayleigh-Taylor turbulence. J. Turbul. 2009, 10:N13. ZZZZZZ, 1468-5248, 10.1080/14685240902870448
61. Boffetta G. Mazzino A. Musacchio S. Vozzella L. Kolmogorov scaling and intermittency in Rayleigh-Taylor turbulence. Phys. Rev. E 2009, 79:065301. PLEEE8, 1063-651X, 10.1103/PhysRevE.79.065301
62. Chertkov M. Phenomenology of Rayleigh-Taylor turbulence. Phys. Rev. Lett. 2003, 91:115001. PRLTAO, 0031-9007, 10.1103/PhysRevLett.91.115001
63. Cabot W. Comparison of two- and three-dimensional simulations of miscible Rayleigh-Taylor instability. Phys. Fluids 2006, 18:045101. PHFLE6, 1070-6631, 10.1063/1.2191856
64. Bernstein I.B. Book D.L. Effect of compressibility on the Rayleigh-Taylor instability. Phys. Fluids 1983, 26:453. PHFLE6, 1070-6631, 10.1063/1.864158
65. Lafay M.-.A. Le Creurer B. Gauthier S. Compressibility effects on the Rayleigh-Taylor instability between miscible fluids. Europhys. Lett. 2007, 79:64002. EULEEJ, 0295-5075, 10.1209/0295-5075/79/64002
66. Gauthier S. (private communication).
67. Le Creurer B. Gauthier S. A return toward equilibrium in a 2d Rayleigh-Taylor instability for compressible fluids with a multidomain adaptive Chebyshev method. Theor. Comput. Fluid Dyn. 2008, 22:125. TCFDEP, 0935-4964, 10.1007/s00162-008-0076-3
68. Celani A. Mazzino A. Vozella L. Rayleigh-Taylor turbulence in two dimensions. Phys. Rev. Lett. 2006, 96:134504. PRLTAO, 0031-9007, 10.1103/PhysRevLett.96.134504
69. Celani A. Matsumoto T. Mazzino A. Vergassola M. Scaling and universality in turbulent convection. Phys. Rev. Lett. 2002, 88:054503. PRLTAO, 0031-9007, 10.1103/PhysRevLett.88.054503
70. Ristorcelli J.R. Clark T.T. Rayleigh-Taylor turbulence: Self-similar analysis and direct numerical simulations. J. Fluid Mech. 2004, 507:213. JFLSA7, 0022-1120, 10.1017/S0022112004008286
71. Cabot W.H. Cook A.W. Reynolds number effects on Rayleigh-Taylor instability with possible implications for type Ia supernovae. Nat. Phys. 2006, 2:562. ZZZZZZ, 1745-2473, 10.1038/nphys361
72. Clark T.T. A numerical study of the statistics of a two dimensional Rayleigh-Taylor mixing layer. Phys. Fluids 2003, 15:2413. PHFLE6, 1070-6631, 10.1063/1.1589015
73. Grad H. On the kinetic theory of rarefied gases. Pure Appl. Math. 1949, 2:325. ZZZZZZ, 0079-8185, 10.1002/cpa.3160020402
74. Belletti F. Biferale L. Mantovani F. Schifano S.F. Toschi F. Tripiccione R. Multiphase lattice Boltzmann on the cell broadband engine. Nuovo Cimento Soc. Ital. Fis., C 2009, 32:53. NIFCAS, 0390-5551