Close Search Advanced
Journals
Resources
About Us
Open Access

Truncation Errors, Exact and Heuristic Stability Analysis of Two-Relaxation-Times Lattice Boltzmann Schemes for Anisotropic Advection-Diffusion Equation

Truncation Errors, Exact and Heuristic Stability Analysis of Two-Relaxation-Times Lattice Boltzmann Schemes for Anisotropic Advection-Diffusion Equation
Preview
Add to basket

Year:    2012

Communications in Computational Physics, Vol. 11 (2012), Iss. 5 : pp. 1439–1502

Abstract

This paper establishes relations between the stability and the high-order truncated corrections for modeling of the mass conservation equation with the two-relaxation-times (TRT) collision operator. First we propose a simple method to derive the truncation errors from the exact, central-difference type, recurrence equations of the TRT scheme. They also supply its equivalent three-time-level discretization form. Two different relationships of the two relaxation rates nullify the third (advection) and fourth (pure diffusion) truncation errors, for any linear equilibrium and any velocity set. However, the two relaxation times alone cannot remove the leading-order advection-diffusion error, because of the intrinsic fourth-order numerical diffusion. The truncation analysis is carefully verified for the evolution of concentration waves with the anisotropic diffusion tensors. The anisotropic equilibrium functions are presented in a simple but general form, suitable for the minimal velocity sets and the d2Q9, d3Q13, d3Q15 and d3Q19 velocity sets. All anisotropic schemes are complemented by their exact necessary von Neumann stability conditions and equivalent finite-difference stencils. The sufficient stability conditions are proposed for the most stable (OTRT) family, which enables modeling at any Peclet numbers with the same velocity amplitude. The heuristic stability analysis of the fourth-order truncated corrections extends the optimal stability to larger relationships of the two relaxation rates, in agreement with the exact (one-dimensional) and numerical (multi-dimensional) stability analysis. A special attention is put on the choice of the equilibrium weights. By combining accuracy and stability predictions, several strategies for selecting the relaxation and free-tunable equilibrium parameters are suggested and applied to the evolution of the Gaussian hill.

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.211210.280611a

Communications in Computational Physics, Vol. 11 (2012), Iss. 5 : pp. 1439–1502

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    64

Keywords:   

  1. Mixing and transport enhancement in microchannels by electrokinetic flows with charged surface heterogeneity

    Guan, Yifei | Yang, Tianhang | Wu, Jian

    Physics of Fluids, Vol. 33 (2021), Iss. 4

    https://doi.org/10.1063/5.0047181 [Citations: 34]

  2. Prediction of the moments in advection-diffusion lattice Boltzmann method. I. Truncation dispersion, skewness, and kurtosis

    Ginzburg, Irina

    Physical Review E, Vol. 95 (2017), Iss. 1

    https://doi.org/10.1103/PhysRevE.95.013304 [Citations: 17]

  3. A single-relaxation-time lattice Boltzmann model for anisotropic advection-diffusion equation based on the diffusion velocity flux formulation

    Perko, Janez

    Computational Geosciences, Vol. 22 (2018), Iss. 6 P.1423

    https://doi.org/10.1007/s10596-018-9761-5 [Citations: 4]

  4. Mixed bounce-back boundary scheme of the general propagation lattice Boltzmann method for advection-diffusion equations

    Guo, Xiuya | Chai, Zhenhua | Pang, Shengyong | Zhao, Yong | Shi, Baochang

    Physical Review E, Vol. 99 (2019), Iss. 6

    https://doi.org/10.1103/PhysRevE.99.063316 [Citations: 8]

  5. Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations

    Cui, Shuqi | Hong, Ning | Shi, Baochang | Chai, Zhenhua

    Physical Review E, Vol. 93 (2016), Iss. 4

    https://doi.org/10.1103/PhysRevE.93.043311 [Citations: 40]

  6. Toward a Complete Kinematic Description of Hydraulic Plucking of Fractured Rock

    Gardner, Michael

    Journal of Hydraulic Engineering, Vol. 149 (2023), Iss. 7

    https://doi.org/10.1061/JHEND8.HYENG-13193 [Citations: 4]

  7. Spurious interface and boundary behaviour beyond physical solutions in lattice Boltzmann schemes

    Ginzburg, Irina

    Journal of Computational Physics, Vol. 431 (2021), Iss. P.109986

    https://doi.org/10.1016/j.jcp.2020.109986 [Citations: 8]

  8. On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations

    Anandan, Megala | Raghurama Rao, S.V.

    Computers & Fluids, Vol. 280 (2024), Iss. P.106348

    https://doi.org/10.1016/j.compfluid.2024.106348 [Citations: 0]

  9. Simulation of stratified flows over a ridge using a lattice Boltzmann model

    Wang, Yansen | MacCall, Benjamin T. | Hocut, Christopher M. | Zeng, Xiping | Fernando, Harindra J. S.

    Environmental Fluid Mechanics, Vol. 20 (2020), Iss. 5 P.1333

    https://doi.org/10.1007/s10652-018-9599-3 [Citations: 10]

  10. Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion part I: Derivation and validation

    Geier, Martin | Pasquali, Andrea | Schönherr, Martin

    Journal of Computational Physics, Vol. 348 (2017), Iss. P.862

    https://doi.org/10.1016/j.jcp.2017.05.040 [Citations: 90]

  11. Simulation of High-Viscosity Generalized Newtonian Fluid Flows in the Mixing Section of a Screw Extruder Using the Lattice Boltzmann Model

    Liu, Liguo | Meng, Zhuo | Zhang, Yujing | Sun, Yize

    ACS Omega, Vol. 8 (2023), Iss. 50 P.47991

    https://doi.org/10.1021/acsomega.3c06663 [Citations: 0]

  12. Application and accuracy issues of TRT lattice Boltzmann method for solving elliptic PDEs commonly encountered in heat transfer and fluid flow problems

    Demuth, Cornelius | Mishra, Shekhar | Mendes, Miguel A.A. | Ray, Subhashis | Trimis, Dimosthenis

    International Journal of Thermal Sciences, Vol. 100 (2016), Iss. P.185

    https://doi.org/10.1016/j.ijthermalsci.2015.09.023 [Citations: 10]

  13. Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

    Silva, Goncalo | Talon, Laurent | Ginzburg, Irina

    Journal of Computational Physics, Vol. 335 (2017), Iss. P.50

    https://doi.org/10.1016/j.jcp.2017.01.023 [Citations: 27]

  14. Coarse- and fine-grid numerical behavior of MRT/TRT lattice-Boltzmann schemes in regular and random sphere packings

    Khirevich, Siarhei | Ginzburg, Irina | Tallarek, Ulrich

    Journal of Computational Physics, Vol. 281 (2015), Iss. P.708

    https://doi.org/10.1016/j.jcp.2014.10.038 [Citations: 115]

  15. Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime. II. Application to curved boundaries

    Silva, Goncalo

    Physical Review E, Vol. 98 (2018), Iss. 2

    https://doi.org/10.1103/PhysRevE.98.023302 [Citations: 24]

  16. Lattice Boltzmann method simulation of 3-D natural convection with double MRT model

    Li, Zheng | Yang, Mo | Zhang, Yuwen

    International Journal of Heat and Mass Transfer, Vol. 94 (2016), Iss. P.222

    https://doi.org/10.1016/j.ijheatmasstransfer.2015.11.042 [Citations: 67]

  17. Local boundary reflections in lattice Boltzmann schemes: Spurious boundary layers and their impact on the velocity, diffusion and dispersion

    Ginzburg, Irina | Roux, Laetitia | Silva, Goncalo

    Comptes Rendus. Mécanique, Vol. 343 (2015), Iss. 10-11 P.518

    https://doi.org/10.1016/j.crme.2015.03.004 [Citations: 20]

  18. Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation

    Yoshida, Hiroaki | Kobayashi, Takayuki | Hayashi, Hidemitsu | Kinjo, Tomoyuki | Washizu, Hitoshi | Fukuzawa, Kenji

    Physical Review E, Vol. 90 (2014), Iss. 1

    https://doi.org/10.1103/PhysRevE.90.013303 [Citations: 43]

  19. Discrete effects on some boundary schemes of multiple-relaxation-time lattice Boltzmann model for convection–diffusion equations

    Wu, Yao | Zhao, Yong | Chai, Zhenhua | Shi, Baochang

    Computers & Mathematics with Applications, Vol. 80 (2020), Iss. 3 P.531

    https://doi.org/10.1016/j.camwa.2020.04.003 [Citations: 3]

  20. Taylor dispersion in heterogeneous porous media: Extended method of moments, theory, and modelling with two-relaxation-times lattice Boltzmann scheme

    Vikhansky, Alexander | Ginzburg, Irina

    Physics of Fluids, Vol. 26 (2014), Iss. 2

    https://doi.org/10.1063/1.4864631 [Citations: 31]
  21. The Lattice Boltzmann Method

    Analysis of the Lattice Boltzmann Equation

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

    2017

    https://doi.org/10.1007/978-3-319-44649-3_4 [Citations: 1]

  22. A recursive finite-difference lattice Boltzmann model for the convection–diffusion equation with a source term

    Huang, Changsheng | Chai, Zhenhua | Shi, Baochang

    Applied Mathematics Letters, Vol. 132 (2022), Iss. P.108139

    https://doi.org/10.1016/j.aml.2022.108139 [Citations: 1]

  23. Numerical simulation of heat transfer in packed beds by two population thermal lattice Boltzmann method

    Straka, Robert

    Mechanics & Industry, Vol. 17 (2016), Iss. 2 P.203

    https://doi.org/10.1051/meca/2015071 [Citations: 4]

  24. Discrete effects on the forcing term for the lattice Boltzmann modeling of steady hydrodynamics

    Silva, Goncalo

    Computers & Fluids, Vol. 203 (2020), Iss. P.104537

    https://doi.org/10.1016/j.compfluid.2020.104537 [Citations: 13]

  25. Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues

    Chai, Zhenhua | Yuan, Xiaolei | Shi, Baochang

    Physical Review E, Vol. 108 (2023), Iss. 1

    https://doi.org/10.1103/PhysRevE.108.015304 [Citations: 5]

  26. Equivalent finite difference and partial differential equations for the lattice Boltzmann method

    Fučík, Radek | Straka, Robert

    Computers & Mathematics with Applications, Vol. 90 (2021), Iss. P.96

    https://doi.org/10.1016/j.camwa.2021.03.014 [Citations: 19]

  27. Enhancement of mixed convection heat transfer in a square cavity via a freely moving elastic ring

    Hoseyni, Arsalan | Dadvand, Abdolrahman | Rezazadeh, Sajad | Mohammadi, S. Keivan

    Theoretical and Computational Fluid Dynamics, Vol. 37 (2023), Iss. 1 P.83

    https://doi.org/10.1007/s00162-022-00637-8 [Citations: 2]

  28. Discrete effects on the source term for the lattice Boltzmann modelling of one-dimensional reaction–diffusion equations

    Silva, Goncalo

    Computers & Fluids, Vol. 251 (2023), Iss. P.105735

    https://doi.org/10.1016/j.compfluid.2022.105735 [Citations: 10]

  29. Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations

    Shang, Jinlong | Chai, Zhenhua | Wang, Huili | Shi, Baochang

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

    https://doi.org/10.1103/PhysRevE.101.023306 [Citations: 10]

  30. A block triple-relaxation-time lattice Boltzmann model for nonlinear anisotropic convection–diffusion equations

    Zhao, Yong | Wu, Yao | Chai, Zhenhua | Shi, Baochang

    Computers & Mathematics with Applications, Vol. 79 (2020), Iss. 9 P.2550

    https://doi.org/10.1016/j.camwa.2019.11.018 [Citations: 14]
  31. The Lattice Boltzmann Method

    MRT and TRT Collision Operators

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

    2017

    https://doi.org/10.1007/978-3-319-44649-3_10 [Citations: 3]

  32. Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

    Ilyin, Oleg

    Mathematics, Vol. 11 (2023), Iss. 22 P.4601

    https://doi.org/10.3390/math11224601 [Citations: 0]

  33. A notion of non-negativity preserving relaxation for a mono-dimensional three velocities scheme with relative velocity

    Dubois, François | Graille, Benjamin | Rao, S.V. Raghurama

    Journal of Computational Science, Vol. 47 (2020), Iss. P.101181

    https://doi.org/10.1016/j.jocs.2020.101181 [Citations: 6]

  34. Steady-state two-relaxation-time lattice Boltzmann formulation for transport and flow, closed with the compact multi-reflection boundary and interface-conjugate schemes

    Ginzburg, Irina

    Journal of Computational Science, Vol. 54 (2021), Iss. P.101215

    https://doi.org/10.1016/j.jocs.2020.101215 [Citations: 14]

  35. Construction and Analysis of Lattice Boltzmann Methods Applied to a 1D Convection-Diffusion Equation

    Dellacherie, Stéphane

    Acta Applicandae Mathematicae, Vol. 131 (2014), Iss. 1 P.69

    https://doi.org/10.1007/s10440-013-9850-3 [Citations: 25]

  36. A fractional-step thermal lattice Boltzmann model for high Peclet number flow

    Deng, Lin | Zhang, Yun | Wen, Yanwei | Shan, Bin | Zhou, Huamin

    Computers & Mathematics with Applications, Vol. 70 (2015), Iss. 5 P.1152

    https://doi.org/10.1016/j.camwa.2015.07.006 [Citations: 6]

  37. Two-relaxation-time lattice Boltzmann method and its application to advective-diffusive-reactive transport

    Yan, Zhifeng | Yang, Xiaofan | Li, Siliang | Hilpert, Markus

    Advances in Water Resources, Vol. 109 (2017), Iss. P.333

    https://doi.org/10.1016/j.advwatres.2017.09.003 [Citations: 12]

  38. Analysis of electro-osmotic flow in a microchannel with undulated surfaces

    Yoshida, Hiroaki | Kinjo, Tomoyuki | Washizu, Hitoshi

    Computers & Fluids, Vol. 124 (2016), Iss. P.237

    https://doi.org/10.1016/j.compfluid.2015.05.001 [Citations: 19]

  39. Lattice Boltzmann method for the convection–diffusion equation in curvilinear coordinate systems

    Yoshida, Hiroaki | Nagaoka, Makoto

    Journal of Computational Physics, Vol. 257 (2014), Iss. P.884

    https://doi.org/10.1016/j.jcp.2013.09.035 [Citations: 27]

  40. Multiple-relaxation-time finite-difference lattice Boltzmann model for the nonlinear convection-diffusion equation

    Chen, Xinmeng | Chai, Zhenhua | Shang, Jinlong | Shi, Baochang

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

    https://doi.org/10.1103/PhysRevE.104.035308 [Citations: 2]

  41. Lattice-Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers

    Contrino, Dario | Lallemand, Pierre | Asinari, Pietro | Luo, Li-Shi

    Journal of Computational Physics, Vol. 275 (2014), Iss. P.257

    https://doi.org/10.1016/j.jcp.2014.06.047 [Citations: 87]

  42. Double MRT thermal lattice Boltzmann method for simulating natural convection of low Prandtl number fluids

    Li, Zheng | Yang, Mo | Zhang, Yuwen

    International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 (2016), Iss. 6 P.1889

    https://doi.org/10.1108/HFF-04-2015-0135 [Citations: 17]

  43. Truncation errors and the rotational invariance of three-dimensional lattice models in the lattice Boltzmann method

    Silva, Goncalo | Semiao, Viriato

    Journal of Computational Physics, Vol. 269 (2014), Iss. P.259

    https://doi.org/10.1016/j.jcp.2014.03.027 [Citations: 49]

  44. Multiple-relaxation-time lattice Boltzmann model-based four-level finite-difference scheme for one-dimensional diffusion equations

    Lin, Yuxin | Hong, Ning | Shi, Baochang | Chai, Zhenhua

    Physical Review E, Vol. 104 (2021), Iss. 1

    https://doi.org/10.1103/PhysRevE.104.015312 [Citations: 11]

  45. Multiple anisotropic collisions for advection–diffusion Lattice Boltzmann schemes

    Ginzburg, Irina

    Advances in Water Resources, Vol. 51 (2013), Iss. P.381

    https://doi.org/10.1016/j.advwatres.2012.04.013 [Citations: 50]

  46. MRT-lattice Boltzmann simulation of MHD natural convection of Bingham nanofluid in a C-shaped enclosure with response surface analysis

    Asha, Nur E. Jannat | Molla, Md. Mamun

    Heliyon, Vol. 9 (2023), Iss. 12 P.e22539

    https://doi.org/10.1016/j.heliyon.2023.e22539 [Citations: 2]

  47. Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

    Yahia, Eman | Schupbach, William | Premnath, Kannan N.

    Fluids, Vol. 6 (2021), Iss. 9 P.326

    https://doi.org/10.3390/fluids6090326 [Citations: 11]

  48. A moment conservation-based non-free parameter compressible lattice Boltzmann model and its application for flux evaluation at cell interface

    Yang, L.M. | Shu, C. | Wu, J.

    Computers & Fluids, Vol. 79 (2013), Iss. P.190

    https://doi.org/10.1016/j.compfluid.2013.03.020 [Citations: 40]

  49. Lattice Boltzmann Method for Stochastic Convection-Diffusion Equations

    Zhao, Weifeng | Huang, Juntao | Yong, Wen-An

    SIAM/ASA Journal on Uncertainty Quantification, Vol. 9 (2021), Iss. 2 P.536

    https://doi.org/10.1137/19M1270665 [Citations: 2]

  50. A general fourth-order mesoscopic multiple-relaxation-time lattice Boltzmann model and its macroscopic finite-difference scheme for two-dimensional diffusion equations

    Chen, Ying | Chai, Zhenhua | Shi, Baochang

    Journal of Computational Physics, Vol. 509 (2024), Iss. P.113045

    https://doi.org/10.1016/j.jcp.2024.113045 [Citations: 1]

  51. Determination of the diffusivity, dispersion, skewness and kurtosis in heterogeneous porous flow. Part II: Lattice Boltzmann schemes with implicit interface

    Ginzburg, Irina

    Advances in Water Resources, Vol. 118 (2018), Iss. P.49

    https://doi.org/10.1016/j.advwatres.2018.05.006 [Citations: 6]
  52. The Lattice Boltzmann Method

    Lattice Boltzmann for Advection-Diffusion Problems

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

    2017

    https://doi.org/10.1007/978-3-319-44649-3_8 [Citations: 4]

  53. An automatic approach for the stability analysis of multi-relaxation-time lattice Boltzmann models

    Yang, Jianbin | Zhao, Weifeng | Lin, Ping

    Journal of Computational Physics, Vol. 519 (2024), Iss. P.113432

    https://doi.org/10.1016/j.jcp.2024.113432 [Citations: 0]

  54. A Multiple-Relaxation-Time Lattice Boltzmann Model for General Nonlinear Anisotropic Convection–Diffusion Equations

    Chai, Zhenhua | Shi, Baochang | Guo, Zhaoli

    Journal of Scientific Computing, Vol. 69 (2016), Iss. 1 P.355

    https://doi.org/10.1007/s10915-016-0198-5 [Citations: 128]

  55. Lattice Boltzmann model for diffusion equation with reduced truncation errors: Applications to Gaussian filtering and image processing

    Ilyin, Oleg

    Applied Mathematics and Computation, Vol. 456 (2023), Iss. P.128123

    https://doi.org/10.1016/j.amc.2023.128123 [Citations: 1]

  56. A discrete Hermite moments based multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations

    Wu, Yao | Chai, Zhenhua | Yuan, Xiaolei | Guo, Xiuya | Shi, Baochang

    Computers & Mathematics with Applications, Vol. 156 (2024), Iss. P.218

    https://doi.org/10.1016/j.camwa.2024.01.009 [Citations: 0]

  57. Unified directional parabolic-accurate lattice Boltzmann boundary schemes for grid-rotated narrow gaps and curved walls in creeping and inertial fluid flows

    Ginzburg, Irina | Silva, Goncalo | Marson, Francesco | Chopard, Bastien | Latt, Jonas

    Physical Review E, Vol. 107 (2023), Iss. 2

    https://doi.org/10.1103/PhysRevE.107.025303 [Citations: 0]

  58. Analysis and improvement of Brinkman lattice Boltzmann schemes: Bulk, boundary, interface. Similarity and distinctness with finite elements in heterogeneous porous media

    Ginzburg, Irina | Silva, Goncalo | Talon, Laurent

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

    https://doi.org/10.1103/PhysRevE.91.023307 [Citations: 52]

  59. Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime: Application to plane boundaries

    Silva, Goncalo | Semiao, Viriato

    Physical Review E, Vol. 96 (2017), Iss. 1

    https://doi.org/10.1103/PhysRevE.96.013311 [Citations: 26]

  60. Two-relaxation-time regularized lattice Boltzmann model for convection-diffusion equation with spatially dependent coefficients

    Yu, Yuan | Qin, Zuojian | Yuan, Haizhuan | Shu, Shi

    Applied Mathematics and Computation, Vol. 488 (2025), Iss. P.129135

    https://doi.org/10.1016/j.amc.2024.129135 [Citations: 0]

  61. Linear Bhatnagar–Gross–Krook equations for simulation of linear diffusion equation by lattice Boltzmann method

    Krivovichev, Gerasim V.

    Applied Mathematics and Computation, Vol. 325 (2018), Iss. P.102

    https://doi.org/10.1016/j.amc.2017.12.027 [Citations: 1]

  62. Truncation effect on Taylor–Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability

    Ginzburg, Irina | Roux, Laetitia

    Journal of Computational Physics, Vol. 299 (2015), Iss. P.974

    https://doi.org/10.1016/j.jcp.2015.07.017 [Citations: 26]

  63. Lattice Boltzmann simulations of a single n-butanol drop rising in water

    Komrakova, A. E. | Eskin, D. | Derksen, J. J.

    Physics of Fluids, Vol. 25 (2013), Iss. 4

    https://doi.org/10.1063/1.4800230 [Citations: 18]

  64. Enhanced heat transfer and symmetry breaking in three-dimensional electro-thermo-hydrodynamic convection

    Wang, Qi | Guan, Yifei | Wu, Jian

    Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 237 (2023), Iss. 11 P.2549

    https://doi.org/10.1177/09544062221136677 [Citations: 2]

  65. Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λbounce-back flux scheme

    Ginzburg, Irina

    Physical Review E, Vol. 95 (2017), Iss. 1

    https://doi.org/10.1103/PhysRevE.95.013305 [Citations: 21]

  66. Multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: Modeling, analysis, and elements

    Chai, Zhenhua | Shi, Baochang

    Physical Review E, Vol. 102 (2020), Iss. 2

    https://doi.org/10.1103/PhysRevE.102.023306 [Citations: 98]

  67. Lattice Boltzmann simulations of thermal convective flows in two dimensions

    Wang, Jia | Wang, Donghai | Lallemand, Pierre | Luo, Li-Shi

    Computers & Mathematics with Applications, Vol. 65 (2013), Iss. 2 P.262

    https://doi.org/10.1016/j.camwa.2012.07.001 [Citations: 173]

  68. Flow and transport in the vadose zone: On the impact of partial saturation and Peclet number on non-Fickian, pre-asymptotic dispersion

    Ollivier-Triquet, Emma | Braconnier, Benjamin | Gervais-Couplet, Véronique | Youssef, Souhail | Talon, Laurent | Bauer, Daniela

    Advances in Water Resources, Vol. 191 (2024), Iss. P.104774

    https://doi.org/10.1016/j.advwatres.2024.104774 [Citations: 0]

  69. Analysis of the parametric models of passive scalar transport used in the lattice Boltzmann method

    Krivovichev, Gerasim V.

    Computers & Mathematics with Applications, Vol. 79 (2020), Iss. 5 P.1503

    https://doi.org/10.1016/j.camwa.2019.09.010 [Citations: 4]

  70. Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

    Silva, Goncalo | Ginzburg, Irina

    International Journal for Numerical Methods in Fluids, Vol. 94 (2022), Iss. 12 P.2104

    https://doi.org/10.1002/fld.5138 [Citations: 3]

  71. Two relaxation time lattice Boltzmann method coupled to fast Fourier transform Poisson solver: Application to electroconvective flow

    Guan, Yifei | Novosselov, Igor

    Journal of Computational Physics, Vol. 397 (2019), Iss. P.108830

    https://doi.org/10.1016/j.jcp.2019.07.029 [Citations: 43]

  72. Assessment of the two relaxation time Lattice‐Boltzmann scheme to simulate Stokes flow in porous media

    Talon, L. | Bauer, D. | Gland, N. | Youssef, S. | Auradou, H. | Ginzburg, I.

    Water Resources Research, Vol. 48 (2012), Iss. 4

    https://doi.org/10.1029/2011WR011385 [Citations: 88]

  73. Parametric schemes for the simulation of the advection process in finite-difference-based single-relaxation-time lattice Boltzmann methods

    Krivovichev, Gerasim V.

    Journal of Computational Science, Vol. 44 (2020), Iss. P.101151

    https://doi.org/10.1016/j.jocs.2020.101151 [Citations: 6]

  74. A Parallel Cellular Automata Lattice Boltzmann Method for Convection-Driven Solidification

    Kao, Andrew | Krastins, Ivars | Alexandrakis, Matthaios | Shevchenko, Natalia | Eckert, Sven | Pericleous, Koulis

    JOM, Vol. 71 (2019), Iss. 1 P.48

    https://doi.org/10.1007/s11837-018-3195-3 [Citations: 25]
  75. The Lattice Boltzmann Method

    Boundary and Initial Conditions

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

    2017

    https://doi.org/10.1007/978-3-319-44649-3_5 [Citations: 0]

  76. Two-relaxation time lattice Boltzmann models for the ion transport equation in electrohydrodynamic flow: D2Q5 vs D2Q9 and D3Q7 vs D3Q27

    Zhu, Baojie | Guan, Yifei | Wu, Jian

    Physics of Fluids, Vol. 33 (2021), Iss. 4

    https://doi.org/10.1063/5.0042564 [Citations: 7]

  77. Implicit-correction-based immersed boundary–lattice Boltzmann method with two relaxation times

    Seta, Takeshi | Rojas, Roberto | Hayashi, Kosuke | Tomiyama, Akio

    Physical Review E, Vol. 89 (2014), Iss. 2

    https://doi.org/10.1103/PhysRevE.89.023307 [Citations: 44]

  78. Fourth-order multiple-relaxation-time lattice Boltzmann model and equivalent finite-difference scheme for one-dimensional convection-diffusion equations

    Chen, Ying | Chai, Zhenhua | Shi, Baochang

    Physical Review E, Vol. 107 (2023), Iss. 5

    https://doi.org/10.1103/PhysRevE.107.055305 [Citations: 6]

  79. Monotonic instability and overstability in two-dimensional electrothermohydrodynamic flow

    Guan, Yifei | He, Xuerao | Wang, Qi | Song, Zhiwei | Zhang, Mengqi | Wu, Jian

    Physical Review Fluids, Vol. 6 (2021), Iss. 1

    https://doi.org/10.1103/PhysRevFluids.6.013702 [Citations: 20]

  80. Multiple-relaxation-time lattice Boltzmann simulation for flow, mass transfer, and adsorption in porous media

    Ma, Qiang | Chen, Zhenqian | Liu, Hao

    Physical Review E, Vol. 96 (2017), Iss. 1

    https://doi.org/10.1103/PhysRevE.96.013313 [Citations: 21]

  81. Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes

    Zhang, Mengxin | Zhao, Weifeng | Lin, Ping

    Journal of Computational Physics, Vol. 389 (2019), Iss. P.147

    https://doi.org/10.1016/j.jcp.2019.03.045 [Citations: 33]

  82. Analytical and numerical investigation of the advective and dispersive transport in Herschel–Bulkley fluids by means of a Lattice–Boltzmann Two-Relaxation-Time scheme

    Batôt, G. | Talon, L. | Peysson, Y. | Fleury, M. | Bauer, D.

    Chemical Engineering Science, Vol. 141 (2016), Iss. P.271

    https://doi.org/10.1016/j.ces.2015.11.017 [Citations: 9]

  83. Two-relaxation-time lattice Boltzmann model of the velocity profiles and volumetric flow rate of generalized Newtonian fluids in a single-screw extruder

    Meng, Zhuo | Liu, Liguo | Zhang, Yujing | Sun, Yize

    AIP Advances, Vol. 14 (2024), Iss. 1

    https://doi.org/10.1063/5.0188122 [Citations: 0]

  84. Macroscopic finite-difference scheme and modified equations of the general propagation multiple-relaxation-time lattice Boltzmann model

    Chen, Ying | Liu, Xi | Chai, Zhenhua | Shi, Baochang

    Physical Review E, Vol. 109 (2024), Iss. 6

    https://doi.org/10.1103/PhysRevE.109.065305 [Citations: 1]

  85. A modified multiple-relaxation-time lattice Boltzmann model for convection–diffusion equation

    Huang, Rongzong | Wu, Huiying

    Journal of Computational Physics, Vol. 274 (2014), Iss. P.50

    https://doi.org/10.1016/j.jcp.2014.05.041 [Citations: 88]

  86. The lattice Boltzmann method for nearly incompressible flows

    Lallemand, Pierre | Luo, Li-Shi | Krafczyk, Manfred | Yong, Wen-An

    Journal of Computational Physics, Vol. 431 (2021), Iss. P.109713

    https://doi.org/10.1016/j.jcp.2020.109713 [Citations: 64]