Close Search Advanced
Journals
Resources
About Us
Open Access

Improved Lattice Boltzmann Without Parasitic Currents for Rayleigh-Taylor Instability

Improved Lattice Boltzmann Without Parasitic Currents for Rayleigh-Taylor Instability
Preview
Add to basket

Year:    2010

Communications in Computational Physics, Vol. 7 (2010), Iss. 3 : pp. 423–444

Abstract

Over the last decade the Lattice Boltzmann Method (LBM) has gained significant interest as a numerical solver for multiphase flows. However most of the LB variants proposed to date are still faced with discreteness artifacts in the form of spurious currents around fluid-fluid interfaces. In the recent past, Lee et al. have proposed a new LB scheme, based on a higher order differencing of the non-ideal forces, which appears to virtually free of spurious currents for a number of representative situations. In this paper, we analyze the Lee method and show that, although strictly speaking, it lacks exact mass conservation, in actual simulations, the mass-breaking terms exhibit a self-stabilizing dynamics which leads to their disappearance in the long-term evolution. This property is specifically demonstrated for the case of a moving droplet at low-Weber number, and contrasted with the behaviour of the Shan-Chen model. Furthermore, the Lee scheme is for the first time applied to the problem of gravity-driven Rayleigh-Taylor instability. Direct comparison with literature data for different values of the Reynolds number, shows again satisfactory agreement. A grid-sensitivity study shows that, while large grids are required to converge the fine-scale details, the large-scale features of the flow settle-down at relatively low resolution. We conclude that the Lee method provides a viable technique for the simulation of Rayleigh-Taylor instabilities on a significant parameter range of Reynolds and Weber numbers.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2009.09.018

Communications in Computational Physics, Vol. 7 (2010), Iss. 3 : pp. 423–444

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:   

  1. Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

    Lin, Chuandong | Xu, Aiguo | Zhang, Guangcai | Luo, Kai Hong | Li, Yingjun

    Physical Review E, Vol. 96 (2017), Iss. 5

    https://doi.org/10.1103/PhysRevE.96.053305 [Citations: 43]

  2. Application of the lattice Boltzmann method for large‐scale hydraulic problems

    Massarotti, Nicola | Biscarini, Chiara | Di Francesco, Silvia | Mencattini, Matteo

    International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 (2011), Iss. 5 P.584

    https://doi.org/10.1108/09615531111135846 [Citations: 17]

  3. Effects of density and force discretizations on spurious velocities in lattice Boltzmann equation for two-phase flows

    Xiong, Yuan | Guo, Zhaoli

    Journal of Physics A: Mathematical and Theoretical, Vol. 47 (2014), Iss. 19 P.195502

    https://doi.org/10.1088/1751-8113/47/19/195502 [Citations: 5]

  4. Phase-field lattice Boltzmann model for interface tracking of a binary fluid system based on the Allen-Cahn equation

    Zu, Y. Q. | Li, A. D. | Wei, H.

    Physical Review E, Vol. 102 (2020), Iss. 5

    https://doi.org/10.1103/PhysRevE.102.053307 [Citations: 21]

  5. On the Stability of the Finite Difference based Lattice Boltzmann Method

    El-Amin, M.F. | Sun, S. | Salama, A.

    Procedia Computer Science, Vol. 18 (2013), Iss. P.2101

    https://doi.org/10.1016/j.procs.2013.05.380 [Citations: 12]

  6. Numerical simulation of dissolved air flotation using a lattice Boltzmann method

    Ghorbanpour-Arani, Amirabbas | Rahimian, Mohammad-Hassan | Haghani-Hassan-Abadi, Reza

    Physical Review E, Vol. 101 (2020), Iss. 2

    https://doi.org/10.1103/PhysRevE.101.023105 [Citations: 6]

  7. Force imbalance in lattice Boltzmann equation for two-phase flows

    Guo, Zhaoli | Zheng, Chuguang | Shi, Baochang

    Physical Review E, Vol. 83 (2011), Iss. 3

    https://doi.org/10.1103/PhysRevE.83.036707 [Citations: 118]

  8. Numerical Study on Bubble Rising in Complex Channels Saturated with Liquid Using a Phase-Field Lattice-Boltzmann Method

    Yu, Kang | Yong, Yumei | Yang, Chao

    Processes, Vol. 8 (2020), Iss. 12 P.1608

    https://doi.org/10.3390/pr8121608 [Citations: 7]

  9. Investigation of two-phase flow in porous media using lattice Boltzmann method

    Taghilou, Mohammad | Rahimian, Mohammad Hassan

    Computers & Mathematics with Applications, Vol. 67 (2014), Iss. 2 P.424

    https://doi.org/10.1016/j.camwa.2013.08.005 [Citations: 24]

  10. Spurious velocity from the cutoff and magnification equation in free energy-based LBM for two-phase flow with a large density ratio

    Gong, Jiaming | Oshima, Nobuyuki | Tabe, Yutaka

    Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 4 P.1166

    https://doi.org/10.1016/j.camwa.2016.08.033 [Citations: 11]

  11. A mass-conserving lattice Boltzmann method for bubble behavior estimation

    Li, Xue | Gao, Deyang | Hou, Baolin | Wang, Xiaodong

    Chemical Engineering Science, Vol. 193 (2019), Iss. P.76

    https://doi.org/10.1016/j.ces.2018.08.061 [Citations: 12]

  12. Finite volume formulation of thermal lattice Boltzmann method

    Zarghami, Ahad | Ubertini, Stefano | Succi, Sauro

    International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 (2014), Iss. 2 P.270

    https://doi.org/10.1108/HFF-11-2011-0234 [Citations: 22]

  13. A review of spurious currents in the lattice Boltzmann method for multiphase flows

    Connington, Kevin | Lee, Taehun

    Journal of Mechanical Science and Technology, Vol. 26 (2012), Iss. 12 P.3857

    https://doi.org/10.1007/s12206-012-1011-5 [Citations: 100]

  14. Lattice-Boltzmann modeling of buoyancy-driven turbulent flows

    Taha, M. | Zhao, S. | Lamorlette, A. | Consalvi, J. L. | Boivin, P.

    Physics of Fluids, Vol. 34 (2022), Iss. 5

    https://doi.org/10.1063/5.0088409 [Citations: 10]

  15. Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios

    Fakhari, Abbas | Bolster, Diogo

    Journal of Computational Physics, Vol. 334 (2017), Iss. P.620

    https://doi.org/10.1016/j.jcp.2017.01.025 [Citations: 137]

  16. Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows

    Li, Q. | Luo, K. H. | Li, X. J.

    Physical Review E, Vol. 86 (2012), Iss. 1

    https://doi.org/10.1103/PhysRevE.86.016709 [Citations: 220]

  17. Finite-volume lattice Boltzmann modeling of thermal transport in nanofluids

    Zarghami, A. | Ubertini, S. | Succi, S.

    Computers & Fluids, Vol. 77 (2013), Iss. P.56

    https://doi.org/10.1016/j.compfluid.2013.02.018 [Citations: 31]

  18. A comparison between different fractal grid generation methods coupled with lattice Boltzmann approach

    Chiappini, D. | Donno, A.

    (2016) P.270003

    https://doi.org/10.1063/1.4952042 [Citations: 3]
  19. Multiphase Lattice Boltzmann Methods: Theory and Application

    References

    2015

    https://doi.org/10.1002/9781118971451.refs [Citations: 0]

  20. Lattice Boltzmann method for Lennard-Jones fluids based on the gradient theory of interfaces

    Kikkinides, E. S. | Kainourgiakis, M. E. | Yiotis, A. G. | Stubos, A. K.

    Physical Review E, Vol. 82 (2010), Iss. 5

    https://doi.org/10.1103/PhysRevE.82.056705 [Citations: 4]

  21. A novel phase-field lattice Boltzmann framework for diffusion-driven multiphase evaporation

    Mirhoseini, Masoumeh | Banaee, Alireza | Jalali, Alireza

    Physics of Fluids, Vol. 36 (2024), Iss. 8

    https://doi.org/10.1063/5.0218145 [Citations: 1]

  22. On the Simulations of Thermal Liquid Foams Using Lattice Boltzmann Method

    Mobarak, Mohammad | Gatternig, Bernhard | Delgado, Antonio

    Energies, Vol. 16 (2022), Iss. 1 P.195

    https://doi.org/10.3390/en16010195 [Citations: 1]

  23. Water impact on obstacles using KBC-free surface lattice Boltzmann method

    Chiappini, Daniele | Di Ilio, Giovanni

    (2018) P.420002

    https://doi.org/10.1063/1.5044005 [Citations: 2]

  24. Detailed Simulation of Complex Hydraulic Problems with Macroscopic and Mesoscopic Mathematical Methods

    Biscarini, Chiara | Di Francesco, Silvia | Nardi, Fernando | Manciola, Piergiorgio

    Mathematical Problems in Engineering, Vol. 2013 (2013), Iss. P.1

    https://doi.org/10.1155/2013/928309 [Citations: 24]

  25. Lattice Boltzmann Finite Volume Formulation with Improved Stability

    Zarghami, A. | Maghrebi, M. J. | Ghasemi, J. | Ubertini, S.

    Communications in Computational Physics, Vol. 12 (2012), Iss. 1 P.42

    https://doi.org/10.4208/cicp.151210.140711a [Citations: 30]

  26. Modeling liquid break-up through a kinetic approach

    Bella, G. | Chiappini, D. | Ubertini, S.

    SAE International Journal of Engines, Vol. 2 (2009), Iss. 2 P.390

    https://doi.org/10.4271/2009-24-0023 [Citations: 8]
  27. The Lattice Boltzmann Method

    Multiphase and Multicomponent Flows

    Krüger, Timm | Kusumaatmaja, Halim | Kuzmin, Alexandr | Shardt, Orest | Silva, Goncalo | Viggen, Erlend Magnus

    2017

    https://doi.org/10.1007/978-3-319-44649-3_9 [Citations: 3]

  28. A lattice Boltzmann method for immiscible two-phase Stokes flow with a local collision operator

    Tölke, Jonas | Prisco, Giuseppe De | Mu, Yaoming

    Computers & Mathematics with Applications, Vol. 65 (2013), Iss. 6 P.864

    https://doi.org/10.1016/j.camwa.2012.05.018 [Citations: 23]

  29. Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

    Kikkinides, E. S. | Monson, P. A.

    The Journal of Chemical Physics, Vol. 142 (2015), Iss. 9

    https://doi.org/10.1063/1.4913636 [Citations: 12]

  30. Ligament break-up simulation through pseudo-potential lattice Boltzmann method

    Chiappini, Daniele | Xue, Xiao | Falcucci, Giacomo | Sbragaglia, Mauro

    (2018) P.420003

    https://doi.org/10.1063/1.5044006 [Citations: 5]

  31. Modification of the phase-field model to reach a high-density ratio and tunable surface tension of two-phase flow using the lattice Boltzmann method

    Taghilou, Mohammad | Shakibaei, Aida

    Acta Mechanica, Vol. 233 (2022), Iss. 12 P.5299

    https://doi.org/10.1007/s00707-022-03376-3 [Citations: 0]

  32. Effects of force discretization on mass conservation in lattice Boltzmann equation for two-phase flows

    Lou, Q. | Guo, Z. L. | Shi, B. C.

    EPL (Europhysics Letters), Vol. 99 (2012), Iss. 6 P.64005

    https://doi.org/10.1209/0295-5075/99/64005 [Citations: 36]

  33. Fluctuating multicomponent lattice Boltzmann model

    Belardinelli, D. | Sbragaglia, M. | Biferale, L. | Gross, M. | Varnik, F.

    Physical Review E, Vol. 91 (2015), Iss. 2

    https://doi.org/10.1103/PhysRevE.91.023313 [Citations: 16]

  34. Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows

    Liang, H. | Shi, B. C. | Guo, Z. L. | Chai, Z. H.

    Physical Review E, Vol. 89 (2014), Iss. 5

    https://doi.org/10.1103/PhysRevE.89.053320 [Citations: 189]

  35. Langevin theory of fluctuations in the discrete Boltzmann equation

    Gross, M | Cates, M E | Varnik, F | Adhikari, R

    Journal of Statistical Mechanics: Theory and Experiment, Vol. 2011 (2011), Iss. 03 P.P03030

    https://doi.org/10.1088/1742-5468/2011/03/P03030 [Citations: 19]

  36. Collision Dynamics and Internal Mixing of Droplets of Non-Newtonian Liquids

    Sun, Kai | Zhang, Peng | Law, Chung K. | Wang, Tianyou

    Physical Review Applied, Vol. 4 (2015), Iss. 5

    https://doi.org/10.1103/PhysRevApplied.4.054013 [Citations: 29]

  37. Modified phase-field-based lattice Boltzmann model for incompressible multiphase flows

    Xu, Xingchun | Hu, Yanwei | Dai, Bing | Yang, Lei | Han, Jiecai | He, Yurong | Zhu, Jiaqi

    Physical Review E, Vol. 104 (2021), Iss. 3

    https://doi.org/10.1103/PhysRevE.104.035305 [Citations: 12]

  38. Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts

    Zu, Y. Q. | He, S.

    Physical Review E, Vol. 87 (2013), Iss. 4

    https://doi.org/10.1103/PhysRevE.87.043301 [Citations: 242]

  39. Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales

    Falcucci, Giacomo | Ubertini, Stefano | Biscarini, Chiara | Francesco, Silvia Di | Chiappini, Daniele | Palpacelli, Silvia | Maio, Alessandro De | Succi, Sauro

    Communications in Computational Physics, Vol. 9 (2011), Iss. 2 P.269

    https://doi.org/10.4208/cicp.221209.250510a [Citations: 62]

  40. Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

    Li, Q. | Luo, K.H. | Kang, Q.J. | He, Y.L. | Chen, Q. | Liu, Q.

    Progress in Energy and Combustion Science, Vol. 52 (2016), Iss. P.62

    https://doi.org/10.1016/j.pecs.2015.10.001 [Citations: 749]

  41. Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method

    Safari, Hesameddin | Rahimian, Mohammad Hassan | Krafczyk, Manfred

    Physical Review E, Vol. 90 (2014), Iss. 3

    https://doi.org/10.1103/PhysRevE.90.033305 [Citations: 61]

  42. Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows

    Li, Q. | Luo, K. H. | Gao, Y. J. | He, Y. L.

    Physical Review E, Vol. 85 (2012), Iss. 2

    https://doi.org/10.1103/PhysRevE.85.026704 [Citations: 101]

  43. Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows

    Liu, Haihu | Valocchi, Albert J. | Zhang, Yonghao | Kang, Qinjun

    Physical Review E, Vol. 87 (2013), Iss. 1

    https://doi.org/10.1103/PhysRevE.87.013010 [Citations: 101]

  44. Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio

    Ba, Yan | Liu, Haihu | Li, Qing | Kang, Qinjun | Sun, Jinju

    Physical Review E, Vol. 94 (2016), Iss. 2

    https://doi.org/10.1103/PhysRevE.94.023310 [Citations: 107]

  45. Shear stress in nonideal fluid lattice Boltzmann simulations

    Gross, Markus | Moradi, Nasrollah | Zikos, Georgios | Varnik, Fathollah

    Physical Review E, Vol. 83 (2011), Iss. 1

    https://doi.org/10.1103/PhysRevE.83.017701 [Citations: 24]

  46. Pattern formation in liquid-vapor systems under periodic potential and shear

    Coclite, A. | Gonnella, G. | Lamura, A.

    Physical Review E, Vol. 89 (2014), Iss. 6

    https://doi.org/10.1103/PhysRevE.89.063303 [Citations: 15]

  47. Multiphase cascaded lattice Boltzmann method

    Lycett-Brown, Daniel | Luo, Kai H.

    Computers & Mathematics with Applications, Vol. 67 (2014), Iss. 2 P.350

    https://doi.org/10.1016/j.camwa.2013.08.033 [Citations: 73]

  48. Local hybrid Allen-Cahn model in phase-field lattice Boltzmann method for incompressible two-phase flow

    Kang, Dong Hun | Yun, Tae Sup

    Physical Review E, Vol. 105 (2022), Iss. 4

    https://doi.org/10.1103/PhysRevE.105.045307 [Citations: 3]

  49. Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model

    Leclaire, Sébastien | Reggio, Marcelo | Trépanier, Jean-Yves

    Computers & Fluids, Vol. 48 (2011), Iss. 1 P.98

    https://doi.org/10.1016/j.compfluid.2011.04.001 [Citations: 70]