Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T17:33:24.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

Published online by Cambridge University Press:  03 November 2022

Yanbiao Gan Open the ORCID record for Yanbiao Gan [Opens in a new window] ,
Aiguo Xu Open the ORCID record for Aiguo Xu [Opens in a new window] ,
Huilin Lai Open the ORCID record for Huilin Lai [Opens in a new window] ,
Wei Li ,
Guanglan Sun  and
Sauro Succi Open the ORCID record for Sauro Succi [Opens in a new window]
Yanbiao Gan
Affiliation:
Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle, School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, PR China
Aiguo Xu*
Affiliation:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, PO Box 8009-26, Beijing 100088, PR China State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, PR China HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, PR China
Huilin Lai
Affiliation:
College of Mathematics and Statistics, FJKLMAA, Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University, Fuzhou 350117, PR China
Wei Li
Affiliation:
Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle, School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, PR China
Guanglan Sun
Affiliation:
Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle, School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, PR China School of Physics, Beijing Institute of Technology, Beijing 100081, PR China
Sauro Succi
Affiliation:
Center for Life Nano Science at La Sapienza, Fondazione Istituto Italiano di Tecnologia, Viale Regina Margherita 295, 00161, Roma, Italy Physics Department and Institute for Applied Computational Science, John A. Paulson School of Applied Science and Engineering, Harvard University, Oxford Street 29, Cambridge, MA 02138, USA
*
†Email address for correspondence: Xu_Aiguo@iapcm.ac.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The aim of this paper is twofold: the first aim is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow regime; the second aim is to present some new insights into the thermo-hydrodynamic non-equilibrium (THNE) effects in the phase separation process. Methodologically, for bulk flow, DBM includes three main pillars: (i) the determination of the fewest kinetic moment relations, which are required by the description of significant THNE effects beyond the realm of continuum fluid mechanics; (ii) the construction of an appropriate discrete equilibrium distribution function recovering all the desired kinetic moments; (iii) the detection, description, presentation and analysis of THNE based on the moments of the non-equilibrium distribution ( $f-f^{(eq)}$). The incorporation of appropriate additional higher-order thermodynamic kinetic moments considerably extends the DBM's capability of handling larger values of the liquid–vapour density ratio, curbing spurious currents, and ensuring mass/momentum/energy conservation. Compared with the DBM with only first-order THNE (Gan et al., Soft Matt., vol. 11 (26), 2015, pp. 5336–5345), the model retrieves kinetic moments beyond the third-order super-Burnett level, and is accurate for weak, moderate and strong THNE cases even when the local Knudsen number exceeds $1/3$. Physically, the ending point of the linear relation between THNE and the concerned physical parameter provides a distinct criterion to identify whether the system is near or far from equilibrium. Besides, the surface tension suppresses the local THNE around the interface, but expands the THNE range and strengthens the THNE intensity away from the interface through interface smoothing and widening.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 951 , 25 November 2022 , A8
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aarts, D.G.A.L., Schmidt, M. & Lekkerkerker, H.N.W. 2004 Direct visual observation of thermal capillary waves. Science 304 (5672), 847–850.CrossRefGoogle ScholarPubMed
Ambruş, V.E., Busuioc, S., Wagner, A.J., Paillusson, F. & Kusumaatmaja, H. 2019 Multicomponent flow on curved surfaces: a vielbein lattice Boltzmann approach. Phys. Rev. E 100 (6), 063306.CrossRefGoogle ScholarPubMed
Ambruş, V.E. & Sofonea, V. 2016 Lattice Boltzmann models based on half-range Gauss–Hermite quadratures. J.Comput. Phys. 316, 760–788.CrossRefGoogle Scholar
Ansumali, S., Karlin, I.V., Arcidiacono, S., Abbas, A. & Prasianakis, N.I. 2007 Hydrodynamics beyond Navier–Stokes: exact solution to the lattice Boltzmann hierarchy. Phy. Rev. Lett. 98 (12), 124502.CrossRefGoogle Scholar
Bao, Y., Qiu, R., Zhou, K., Zhou, T., Weng, Y., Lin, K. & You, Y. 2022 Study of shock wave/boundary layer interaction from the perspective of nonequilibrium effects. Phys. Fluids 34 (4), 046109.CrossRefGoogle Scholar
Bedeaux, D. 1986 Nonequilibrium thermodynamics and statistical physics of surfaces. Adv. Chem. Phys. 64, 47–109.Google Scholar
Benzi, R., Biferale, L., Sbragaglia, M., Succi, S. & Toschi, F. 2006 Mesoscopic two-phase model for describing apparent slip in micro-channel flows. Europhys. Lett. 74 (4), 651.CrossRefGoogle Scholar
Benzi, R., Succi, S. & Vergassola, M. 1992 The lattice Boltzmann equation: theory and applications. Phys. Rep. 222 (3), 145–197.CrossRefGoogle Scholar
Bernaschi, M., Melchionna, S. & Succi, S. 2019 Mesoscopic simulations at the physics–chemistry–biology interface. Rev. Mod. Phys. 91 (2), 025004.CrossRefGoogle Scholar
Bhairapurada, K., Denet, B. & Boivin, P. 2022 A lattice-Boltzmann study of premixed flames thermo-acoustic instabilities. Combust. Flame 240, 112049.CrossRefGoogle Scholar
Bhatnagar, P.L., Gross, E.P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (3), 511.CrossRefGoogle Scholar
Biferale, L., Perlekar, P., Sbragaglia, M. & Toschi, F. 2012 Convection in multiphase fluid flows using lattice Boltzmann methods. Phys. Rev. Lett. 108 (10), 104502.CrossRefGoogle ScholarPubMed
Brennen, C.E. 2005 Fundamentals of Multiphase Flow. Cambridge University Press.CrossRefGoogle Scholar
Bu, W., Kim, D. & Vaknin, D. 2014 Density profiles of liquid/vapor interfaces away from their critical points. J.Phys. Chem. C 118 (23), 12405–12409.CrossRefGoogle Scholar
Busuioc, S., Ambruş, V.E., Biciuşcă, T. & Sofonea, V. 2020 Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature. Comput. Maths Applics. 79 (1), 111–140.CrossRefGoogle Scholar
Carenza, L.N., Gonnella, G., Marenduzzo, D. & Negro, G. 2019 Rotation and propulsion in 3D active chiral droplets. Proc. Natl Acad. Sci. 116 (44), 22065–22070.CrossRefGoogle ScholarPubMed
Carnahan, N.F. & Starling, K.E. 1969 Equation of state for nonattracting rigid spheres. J.Chem. Phys. 51 (2), 635–636.CrossRefGoogle Scholar
Cates, M.E., Fielding, S.M., Marenduzzo, D., Orlandini, E. & Yeomans, J.M. 2008 Shearing active gels close to the isotropic-nematic transition. Phys. Rev. Lett. 101 (6), 068102.CrossRefGoogle Scholar
Chai, Z., Huang, C., Shi, B. & Guo, Z. 2016 A comparative study on the lattice Boltzmann models for predicting effective diffusivity of porous media. Intl J. Heat Mass Transfer 98, 687–696.CrossRefGoogle Scholar
Chai, Z., Liang, H., Du, R. & Shi, B. 2019 A lattice Boltzmann model for two-phase flow in porous media. SIAM J. Sci. Comput. 41 (4), B746–B772.CrossRefGoogle Scholar
Chai, Z. & Shi, B. 2008 A novel lattice Boltzmann model for the Poisson equation. Appl. Math. Model. 32 (10), 2050–2058.CrossRefGoogle Scholar
Chapman, S. & Cowling, T.G. 1990 The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. Cambridge University Press.Google Scholar
Chen, X., Chai, Z., Shang, J. & Shi, B. 2021 b Multiple-relaxation-time finite-difference lattice Boltzmann model for the nonlinear convection–diffusion equation. Phys. Rev. E 104 (3), 035308.CrossRefGoogle ScholarPubMed
Chen, Y. & Deng, Z. 2017 Hydrodynamics of a droplet passing through a microfluidic T-junction. J.Fluid Mech. 819, 401–434.CrossRefGoogle Scholar
Chen, S. & Doolen, G.D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30 (1), 329–364.CrossRefGoogle Scholar
Chen, L., Kang, Q., Tang, Q., Robinson, B.A., He, Y. & Tao, W. 2015 Pore-scale simulation of multicomponent multiphase reactive transport with dissolution and precipitation. Intl J. Heat Mass Transfer 85, 935–949.CrossRefGoogle Scholar
Chen, L., Kang, Q. & Tao, W. 2021 a Pore-scale numerical study of multiphase reactive transport processes in cathode catalyst layers of proton exchange membrane fuel cells. Intl J. Hydrogen Energy 46 (24), 13283–13297.CrossRefGoogle Scholar
Chen, Z., Shu, C., Yang, L.M., Zhao, X. & Liu, N.Y. 2021 c Phase-field-simplified lattice Boltzmann method for modeling solid–liquid phase change. Phys. Rev. E 103 (2), 023308.CrossRefGoogle ScholarPubMed
Chen, T., Wu, L., Wang, L. & Chen, S. 2022 b Rarefaction effects in head-on collision of two identical droplets. Preprint. arXiv:2205.03604.Google Scholar
Chen, F., Xu, A., Zhang, Y., Gan, Y., Liu, B. & Wang, S. 2022 a Delineation of the flow and mixing induced by Rayleigh–Taylor instability through tracers. Front. Phys. 17 (3), 33505.CrossRefGoogle Scholar
Chen, F., Xu, A., Zhang, Y. & Zeng, Q. 2020 Morphological and non-equilibrium analysis of coupled Rayleigh–Taylor–Kelvin–Helmholtz instability. Phys. Fluids 32 (10), 104111.CrossRefGoogle Scholar
Chen, Q., Zhang, X. & Zhang, J. 2013 Improved treatments for general boundary conditions in the lattice Boltzmann method for convection–diffusion and heat transfer processes. Phys. Rev. E 88 (3), 033304.CrossRefGoogle ScholarPubMed
Chen, W.F., Zhao, W.W., Jiang, Z.Z. & Liui, H.L. 2016 A review of moment equations for rarefied gas dynamics. Phys. Gases 1 (5), 9–24.Google Scholar
Chen, X., Zhong, C. & Yuan, X. 2011 Lattice Boltzmann simulation of cavitating bubble growth with large density ratio. Comput. Maths Applics. 61 (12), 3577–3584.CrossRefGoogle Scholar
Chikatamarla, S.S., Ansumali, S. & Karlin, I.V. 2006 Grad's approximation for missing data in lattice Boltzmann simulations. Europhys. Lett. 74 (2), 215.CrossRefGoogle Scholar
Chikatamarla, S.S. & Karlin, I.V. 2009 Lattices for the lattice Boltzmann method. Phys. Rev. E 79 (4), 046701.CrossRefGoogle ScholarPubMed
Coclite, A., Gonnella, G. & Lamura, A. 2014 Pattern formation in liquid–vapor systems under periodic potential and shear. Phys. Rev. E 89 (6), 063303.CrossRefGoogle ScholarPubMed
Corberi, F., Gonnella, G. & Lamura, A. 1998 Spinodal decomposition of binary mixtures in uniform shear flow. Phys. Rev. Lett. 81 (18), 3852.CrossRefGoogle Scholar
Coreixas, C., Wissocq, G., Puigt, G., Boussuge, J. & Sagaut, P. 2017 Recursive regularization step for high-order lattice Boltzmann methods. Phys. Rev. E 96 (3), 033306.CrossRefGoogle ScholarPubMed
Czelusniak, L.E., Mapelli, V.P., Guzella, M.S., Cabezas-Gómez, L. & Wagner, A.J. 2020 Force approach for the pseudopotential lattice Boltzmann method. Phys. Rev. E 102 (3), 033307.CrossRefGoogle ScholarPubMed
Dai, R., Li, W., Mostaghimi, J., Wang, Q. & Zeng, M. 2020 On the optimal heat source location of partially heated energy storage process using the newly developed simplified enthalpy based lattice Boltzmann method. Appl. Energy 275, 115387.CrossRefGoogle Scholar
Doostmohammadi, A., Adamer, M.F., Thampi, S.P. & Yeomans, J.M. 2016 Stabilization of active matter by flow-vortex lattices and defect ordering. Nat. Commun. 7 (1), 10557.CrossRefGoogle ScholarPubMed
Du, R. & Liu, Z. 2020 A lattice Boltzmann model for the fractional advection–diffusion equation coupled with incompressible Navier–Stokes equation. Appl. Math. Lett. 101, 106074.CrossRefGoogle Scholar
Duan, Y. & Liu, R. 2007 Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation. J.Comput. Appl. Maths 206 (1), 432–439.CrossRefGoogle Scholar
Dupin, M., Halliday, I. & Care, C. 2006 A multi-component lattice Boltzmann scheme: towards the mesoscale simulation of blood flow. Med. Engng Phys. 28 (1), 13–18.CrossRefGoogle ScholarPubMed
Elton, B.H. 1996 Comparisons of lattice Boltzmann and finite difference methods for a two-dimensional viscous Burgers equation. SIAM J. Sci. Comput. 17 (4), 783–813.CrossRefGoogle Scholar
Evans, R. 1979 The nature of the liquid–vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids. Adv. Phys. 28 (2), 143–200.CrossRefGoogle Scholar
Fakhari, A. & Lee, T. 2013 Multiple-relaxation-time lattice Boltzmann method for immiscible fluids at high Reynolds numbers. Phys. Rev. E 87 (2), 023304.CrossRefGoogle ScholarPubMed
Falcucci, G., Amati, G., Fanelli, P., Krastev, V.K., Polverino, G., Porfiri, M. & Succi, S. 2021 Extreme flow simulations reveal skeletal adaptations of deep-sea sponges. Nature 595 (7868), 537–541.CrossRefGoogle ScholarPubMed
Falcucci, G., Chiatti, G., Succi, S., Mohamad, A.A. & Kuzmin, A. 2009 Rupture of a ferrofluid droplet in external magnetic fields using a single-component lattice Boltzmann model for nonideal fluids. Phys. Rev. E 79 (5), 056706.CrossRefGoogle ScholarPubMed
Falcucci, G., Jannelli, E., Ubertini, S. & Succi, S. 2013 Direct numerical evidence of stress-induced cavitation. J.Fluid Mech. 728, 362–375.CrossRefGoogle Scholar
Fei, L., Qin, F., Wang, G., Luo, K.H., Derome, D. & Carmeliet, J. 2022 Droplet evaporation in finite-size systems: theoretical analysis and mesoscopic modeling. Phys. Rev. E 105 (2), 025101.CrossRefGoogle ScholarPubMed
Fei, L., Yang, J., Chen, Y., Mo, H. & Luo, K.H. 2020 Mesoscopic simulation of three-dimensional pool boiling based on a phase-change cascaded lattice Boltzmann method. Phys. Fluids 32 (10), 103312.CrossRefGoogle Scholar
Frezzotti, A. 2011 Boundary conditions at the vapor–liquid interface. Phys. Fluids 23 (3), 030609.CrossRefGoogle Scholar
Frezzotti, A., Barbante, P. & Gibelli, L. 2019 Direct simulation Monte Carlo applications to liquid–vapor flows. Phys. Fluids 31 (6), 062103.CrossRefGoogle Scholar
Frezzotti, A., Gibelli, L., Lockerby, D.A. & Sprittles, J.E. 2018 Mean-field kinetic theory approach to evaporation of a binary liquid into vacuum. Phys. Rev. Fluids 3 (5), 054001.CrossRefGoogle Scholar
Frezzotti, A., Gibelli, L. & Lorenzani, S. 2005 Mean field kinetic theory description of evaporation of a fluid into vacuum. Phys. Fluids 17 (1), 012102.CrossRefGoogle Scholar
Frezzotti, A. & Rossi, M. 2012 Slip effects at the vapor–liquid boundary. AIP Conf. Proc. 1501 (1), 903–910.CrossRefGoogle Scholar
Gan, Y., Xu, A., Zhang, G. & Li, Y. 2012 a Physical modeling of multiphase flow via lattice Boltzmann method: numerical effects, equation of state and boundary conditions. Front. Phys. 7 (4), 481–490.CrossRefGoogle Scholar
Gan, Y., Xu, A., Zhang, G., Li, Y. & Li, H. 2011 Phase separation in thermal systems: a lattice Boltzmann study and morphological characterization. Phys. Rev. E 84 (4), 046715.CrossRefGoogle ScholarPubMed
Gan, Y.B., Xu, A.G., Zhang, G.C., Lin, C.D. & Liu, Z.P. 2019 Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows. Front. Phys. 14 (4), 43602.CrossRefGoogle Scholar
Gan, Y., Xu, A., Zhang, G. & Succi, S. 2015 Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects. Soft Matt. 11 (26), 5336–5345.CrossRefGoogle ScholarPubMed
Gan, Y., Xu, A., Zhang, G. & Yang, Y. 2013 Lattice BGK kinetic model for high-speed compressible flows: hydrodynamic and nonequilibrium behaviors. Europhys. Lett. 103 (2), 24003.CrossRefGoogle Scholar
Gan, Y., Xu, A., Zhang, G., Yu, X. & Li, Y. 2008 Two-dimensional lattice Boltzmann model for compressible flows with high Mach number. Physica A 387 (8–9), 1721–1732.CrossRefGoogle Scholar
Gan, Y., Xu, A., Zhang, G., Zhang, P. & Li, Y. 2012 b Lattice Boltzmann study of thermal phase separation: effects of heat conduction, viscosity and Prandtl number. Europhys. Lett. 97 (4), 44002.CrossRefGoogle Scholar
Gan, Y., Xu, A., Zhang, G., Zhang, Y. & Succi, S. 2018 Discrete Boltzmann trans-scale modeling of high-speed compressible flows. Phys. Rev. E 97 (5), 053312.CrossRefGoogle ScholarPubMed
Gao, W. & Sun, Q. 2014 Evaluation of BGK-type models of the Boltzmann equation. AIP Conf. Proc. 1628 (1), 84–91.CrossRefGoogle Scholar
Gonnella, G., Lamura, A., Piscitelli, A. & Tiribocchi, A. 2010 Phase separation of binary fluids with dynamic temperature. Phys. Rev. E 82 (4), 046302.CrossRefGoogle ScholarPubMed
Gonnella, G., Lamura, A. & Sofonea, V. 2007 Lattice Boltzmann simulation of thermal nonideal fluids. Phys. Rev. E 76 (3), 036703.CrossRefGoogle ScholarPubMed
Gonnella, G., Orlandini, E. & Yeomans, J.M. 1997 Spinodal decomposition to a lamellar phase: effects of hydrodynamic flow. Phys. Rev. Lett. 78 (9), 1695.CrossRefGoogle Scholar
Gunstensen, A.K., Rothman, D.H., Zaleski, S. & Zanetti, G. 1991 Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43 (8), 4320–4327.CrossRefGoogle ScholarPubMed
Guo, Z. & Shu, C. 2013 Lattice Boltzmann Method and its Applications in Engineering. World Scientific Publishing.CrossRefGoogle Scholar
Gurtin, M.E. & Voorhees, P.W. 1996 The thermodynamics of evolving interfaces far from equilibrium. Acta Mater. 44 (1), 235–247.CrossRefGoogle Scholar
He, X., Chen, S. & Zhang, R. 1999 A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability. J.Comput. Phys. 152 (2), 642–663.CrossRefGoogle Scholar
He, Y. & Lin, X. 2020 Numerical analysis and simulations for coupled nonlinear Schrödinger equations based on lattice Boltzmann method. Appl. Maths Lett. 106, 106391.CrossRefGoogle Scholar
He, Y., Liu, Q., Li, Q. & Tao, W. 2019 Lattice Boltzmann methods for single-phase and solid–liquid phase-change heat transfer in porous media: a review. Intl J. Heat Mass Transfer 129, 160–197.CrossRefGoogle Scholar
He, B., Qin, C., Chen, W. & Wen, B. 2022 Numerical simulation of pulmonary airway reopening by the multiphase lattice Boltzmann method. Comput. Maths Applics. 108, 196–205.CrossRefGoogle Scholar
He, X., Shan, X. & Doolen, G.D. 1998 Discrete Boltzmann equation model for nonideal gases. Phys. Rev. E 57 (1), R13–R16.CrossRefGoogle Scholar
He, Q., Tao, S., Yang, X., Lu, W. & He, Z. 2021 Discrete unified gas kinetic scheme simulation of microflows with complex geometries in Cartesian grid. Phys. Fluids 33 (4), 042005.CrossRefGoogle Scholar
Holway, L.H. Jr. 1966 New statistical models for kinetic theory: methods of construction. Phys. Fluids 9 (9), 1658–1673.CrossRefGoogle Scholar
Hu, Y., Li, D. & Niu, X. 2018 Phase-field-based lattice Boltzmann model for multiphase ferrofluid flows. Phys. Rev. E 98 (3), 033301.CrossRefGoogle Scholar
Huang, Q., Tian, F.B., Young, J. & Lai, J.C.S. 2021 a Transition to chaos in a two-sided collapsible channel flow. J.Fluid Mech. 926, A15.CrossRefGoogle Scholar
Huang, R., Wu, H. & Adams, N.A. 2021 b Mesoscopic lattice Boltzmann modeling of the liquid–vapor phase transition. Phys. Rev. Lett. 126 (24), 244501.CrossRefGoogle ScholarPubMed
Jaensson, N. & Vermant, J. 2018 Tensiometry and rheology of complex interfaces. Curr. Opin. Colloid Interface Sci. 37, 136–150.CrossRefGoogle Scholar
Kähler, G., Bonelli, F., Gonnella, G. & Lamura, A. 2015 Cavitation inception of a van der Waals fluid at a sack-wall obstacle. Phys. Fluids 27 (12), 123307.CrossRefGoogle Scholar
Kendon, V.M., Desplat, J.C., Bladon, P. & Cates, M.E. 1999 3D spinodal decomposition in the inertial regime. Phys. Rev. Lett. 83 (3), 576.CrossRefGoogle Scholar
Lai, H. & Ma, C. 2010 The lattice Boltzmann model for the second-order Benjamin–Ono equations. J.Stat. Mech.: Theory Exp. 2010 (4), P04011.CrossRefGoogle Scholar
Lai, H. & Ma, C. 2011 Lattice Boltzmann model for generalized nonlinear wave equations. Phys. Rev. E 84 (4), 046708.CrossRefGoogle ScholarPubMed
Lai, H., Xu, A., Zhang, G., Gan, Y., Ying, Y. & Succi, S. 2016 Non-equilibrium thermo-hydrodynamic effects on the Rayleigh–Taylor instability in compressible flows. Phys. Rev. E 94 (2), 023106.CrossRefGoogle Scholar
Lan, Z.Z., Hu, W.Q. & Guo, B.L. 2019 General propagation lattice Boltzmann model for a variable-coefficient compound KdV–Burgers equation. Appl. Math. Model. 73, 695–714.CrossRefGoogle Scholar
Lang, F. & Leiderer, P. 2006 Liquid–vapour phase transitions at interfaces: sub-nanosecond investigations by monitoring the ejection of thin liquid films. New J. Phys. 8 (1), 14.CrossRefGoogle Scholar
Ledesma-Aguilar, R., Vella, D. & Yeomans, J.M. 2014 Lattice-Boltzmann simulations of droplet evaporation. Soft Matt. 10 (41), 8267.CrossRefGoogle ScholarPubMed
Li, W., Li, Q., Yu, Y. & Wen, Z. 2020 Enhancement of nucleate boiling by combining the effects of surface structure and mixed wettability: a lattice Boltzmann study. App. Therm. Engng 180, 115849.CrossRefGoogle Scholar
Li, Q., Luo, K.H., Kang, Q.J., He, Y.L., Chen, Q. & Liu, Q. 2016 Lattice Boltzmann methods for multiphase flow and phase-change heat transfer. Prog. Energy Combust. Sci. 52, 62–105.CrossRefGoogle Scholar
Li, A., Luo, Y.X., Liu, Y., Xu, Y.Q., Tian, F.B. & Wang, Y. 2022 Hydrodynamic behaviors of self-propelled sperms in confined spaces. Engng Appl. Comput. Fluid Mech. 16 (1), 141–160.Google Scholar
Li, Z.H., Peng, A.P., Zhang, H.X. & Yang, J.Y. 2015 Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations. Prog. Aerosp. Sci. 74, 81–113.CrossRefGoogle Scholar
Li, X., Shi, Y. & Shan, X. 2019 Temperature-scaled collision process for the high-order lattice Boltzmann model. Phys. Rev. E 100 (1), 013301.CrossRefGoogle ScholarPubMed
Li, Q., Yu, Y., Zhou, P. & Yan, H.J. 2018 Enhancement of boiling heat transfer using hydrophilic–hydrophobic mixed surfaces: a lattice Boltzmann study. Appl. Therm. Engng 132, 490–499.CrossRefGoogle Scholar
Li, Z.H. & Zhang, H.X. 2004 Study on gas kinetic unified algorithm for flows from rarefied transition to continuum. J.Comput. Phys. 193 (2), 708–738.CrossRefGoogle Scholar
Liang, H., Li, Y., Chen, J. & Xu, J. 2019 Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio. Intl J. Heat Mass Transfer 130, 1189–1205.CrossRefGoogle Scholar
Liang, H., Li, Q.X., Shi, B.C. & Chai, Z.H. 2016 a Lattice Boltzmann simulation of three-dimensional Rayleigh–Taylor instability. Phys. Rev. E 93 (3), 033113.CrossRefGoogle ScholarPubMed
Liang, H., Shi, B.C. & Chai, Z.H. 2016 b Lattice Boltzmann modeling of three-phase incompressible flows. Phys. Rev. E 93 (1), 013308.CrossRefGoogle ScholarPubMed
Liang, H., Shi, B.C., Guo, Z.L. & Chai, Z.H. 2014 Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows. Phys. Rev. E 89 (5), 053320.CrossRefGoogle ScholarPubMed
Lin, C., Luo, K.H., Fei, L. & Succi, S. 2017 A multi-component discrete Boltzmann model for nonequilibrium reactive flows. Sci. Rep. 7 (1), 14580.CrossRefGoogle ScholarPubMed
Lin, C., Luo, K.H., Xu, A., Gan, Y. & Lai, H. 2021 Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects. Phys. Rev. E 103 (1), 013305.CrossRefGoogle ScholarPubMed
Lin, C., Xu, A., Zhang, G. & Li, Y. 2016 Double-distribution-function discrete Boltzmann model for combustion. Combust. Flame 164, 137–151.CrossRefGoogle Scholar
Lin, C., Xu, A., Zhang, G., Li, Y. & Succi, S. 2014 Polar coordinate lattice Boltzmann modeling of compressible flows. Phys. Rev. E 89 (1), 013307.CrossRefGoogle ScholarPubMed
Liu, H., Ba, Y., Wu, L., Li, Z., Xi, G. & Zhang, Y. 2018 A hybrid lattice Boltzmann and finite difference method for droplet dynamics with insoluble surfactants. J.Fluid Mech. 837, 381–412.CrossRefGoogle Scholar
Liu, X., Chai, Z. & Shi, B. 2019 A phase-field-based lattice Boltzmann modeling of two-phase electro-hydrodynamic flows. Phys. Fluids 31 (9), 092103.CrossRefGoogle Scholar
Liu, H., Kang, Q., Leonardi, C.R., Schmieschek, S., Narváez, A., Jones, B.D., Williams, J.R., Valocchi, A.J. & Harting, J. 2016 Multiphase lattice Boltzmann simulations for porous media applications. Comput. Geosci. 20 (4), 777–805.CrossRefGoogle Scholar
Liu, F. & Shi, W. 2011 Numerical solutions of two-dimensional Burgers's equations by lattice Boltzmann method. Commun. Nonlinear Sci. Numer. Simul. 16 (1), 150–157.CrossRefGoogle Scholar
Liu, Z., Song, J., Xu, A., Zhang, Y. & Xie, K. 2022 Discrete Boltzmann modeling of plasma shock wave. In Proceedings of the Institution of Mechanical Engineers, Part C. Journal of Mechanical Engineering Science, doi:10.1177/09544062221075943.CrossRefGoogle Scholar
Liu, H., Zhang, Y., Kang, W., Zhang, P., Duan, H. & He, X.T. 2017 Molecular dynamics simulation of strong shock waves propagating in dense deuterium, taking into consideration effects of excited electrons. Phys. Rev. E 95 (2), 023201.CrossRefGoogle ScholarPubMed
Liu, H., Zhou, H., Kang, W., Zhang, P., Duan, H., Zhang, W. & He, X.T. 2020 Dynamics of bond breaking and formation in polyethylene near shock front. Phys. Rev. E 102 (2), 023207.CrossRefGoogle ScholarPubMed
Luo, K.H., Fei, L. & Wang, G. 2021 A unified lattice Boltzmann model and application to multiphase flows. Phil. Trans. R. Soc. A 379 (2208), 20200397.CrossRefGoogle ScholarPubMed
Luo, K.H., Xia, J. & Monaco, E. 2009 Multiscale modeling of multiphase flow with complex interactions. J.Multiscale Model. 1 (1), 125–156.CrossRefGoogle Scholar
Mazloomi M, A., Chikatamarla, S.S. & Karlin, I.V. 2015 Entropic lattice Boltzmann method for multiphase flows. Phys. Rev. Lett. 114 (17), 174502.CrossRefGoogle ScholarPubMed
Milan, F., Biferale, L., Sbragaglia, M. & Toschi, F. 2020 Sub-Kolmogorov droplet dynamics in isotropic turbulence using a multiscale lattice Boltzmann scheme. J.Comput. Sci. 45, 101178.CrossRefGoogle Scholar
Montessori, A., Prestininzi, P., La Rocca, M. & Succi, S. 2015 Lattice Boltzmann approach for complex nonequilibrium flows. Phys. Rev. E 92 (4), 043308.CrossRefGoogle ScholarPubMed
Montessori, A., Prestininzi, P., La Rocca, M. & Succi, S. 2017 Entropic lattice pseudo-potentials for multiphase flow simulations at high Weber and Reynolds numbers. Phys. Fluids 29 (9), 092103.CrossRefGoogle Scholar
Myong, R.S. 1999 Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flows. Phys. Fluids 11 (9), 2788–2802.CrossRefGoogle Scholar
Negro, G., Carenza, L.N., Lamura, A., Tiribocchi, A. & Gonnella, G. 2019 Rheology of active polar emulsions: from linear to unidirectional and inviscid flow, and intermittent viscosity. Soft Matt. 15 (41), 8251–8265.CrossRefGoogle ScholarPubMed
Onuki, A. 2002 Phase Transition Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Onuki, A. 2005 Dynamic van der Waals theory of two-phase fluids in heat flow. Phys. Rev. Lett. 94 (5), 054501.CrossRefGoogle Scholar
Onuki, A. 2007 Dynamic van der Waals theory. Phys. Rev. E 75 (3), 036304.CrossRefGoogle ScholarPubMed
Osborn, W.R., Orlandini, E., Swift, M.R., Yeomans, J.M. & Banavar, J.R. 1995 Lattice Boltzmann study of hydrodynamic spinodal decomposition. Phys. Rev. Lett. 75 (22), 4031.CrossRefGoogle ScholarPubMed
Otomo, H., Boghosian, B.M. & Dubois, F. 2018 Efficient lattice Boltzmann models for the Kuramoto–Sivashinsky equation. Comput. Fluids 172, 683–688.CrossRefGoogle Scholar
Pachalieva, A. & Wagner, A.J. 2021 Connecting lattice Boltzmann methods to physical reality by coarse-graining molecular dynamics simulations. Preprint. arXiv:2109.05009.Google Scholar
Parsa, M.R., Kim, C. & Wagner, A.J. 2021 Nonuniqueness of fluctuating momentum in coarse-grained systems. Phys. Rev. E 104 (1), 015304.CrossRefGoogle ScholarPubMed
Parsa, M.R. & Wagner, A.J. 2017 Lattice gas with molecular dynamics collision operator. Phys. Rev. E 96 (1), 013314.CrossRefGoogle ScholarPubMed
Parsa, M.R. & Wagner, A.J. 2020 Large fluctuations in nonideal coarse-grained systems. Phys. Rev. Lett. 124 (23), 234501.CrossRefGoogle ScholarPubMed
Pelusi, F., Sbragaglia, M., Benzi, R., Scagliarini, A., Bernaschi, M. & Succi, S. 2021 Rayleigh–Bénard convection of a model emulsion: anomalous heat-flux fluctuations and finite-size droplet effects. Soft Matt. 17 (13), 3709–3721.CrossRefGoogle Scholar
Peng, D.Y. & Robinson, D.B. 1976 A new two-constant equation of state. Ind. Engng Chem. Fundam. 15 (1), 59–64.CrossRefGoogle Scholar
Perlekar, P., Benzi, R., Clercx, H.J.H., Nelson, D.R. & Toschi, F. 2014 Spinodal decomposition in homogeneous and isotropic turbulence. Phys. Rev. Lett. 112 (1), 014502.CrossRefGoogle ScholarPubMed
Persad, A.H. & Ward, C.A. 2016 Expressions for the evaporation and condensation coefficients in the Hertz–Knudsen relation. Chem. Rev. 116, 7727–7767.CrossRefGoogle ScholarPubMed
Philippi, P.C., Hegele, L.A., dos Santos, L.O.E. & Surmas, R. 2006 From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models. Phys. Rev. E 73 (5), 056702.CrossRefGoogle Scholar
Qin, F., Del Carro, L., Mazloomi Moqaddam, A., Kang, Q., Brunschwiler, T., Derome, D. & Carmeliet, J. 2019 Study of non-isothermal liquid evaporation in synthetic micro-pore structures with hybrid lattice Boltzmann model. J.Fluid Mech. 866, 33–60.CrossRefGoogle Scholar
Qiu, R., Bao, Y., Zhou, T., Che, H., Chen, R. & You, Y. 2020 Study of regular reflection shock waves using a mesoscopic kinetic approach: curvature pattern and effects of viscosity. Phy. Fluids 32 (10), 106106.CrossRefGoogle Scholar
Qiu, R., Zhou, T., Bao, Y., Zhou, K., Che, H. & You, Y. 2021 Mesoscopic kinetic approach for studying nonequilibrium hydrodynamic and thermodynamic effects of shock wave, contact discontinuity, and rarefaction wave in the unsteady shock tube. Phys. Rev. E 103 (5), 053113.CrossRefGoogle ScholarPubMed
Rana, A.S., Saini, S., Chakraborty, S., Lockerby, D.A. & Sprittles, J.E. 2021 Efficient simulation of non-classical liquid–vapour phase-transition flows: a method of fundamental solutions. J.Fluid Mech. 919, A35.CrossRefGoogle Scholar
Rasin, I., Miller, W. & Succi, S. 2005 Phase-field lattice kinetic scheme for the numerical simulation of dendritic growth. Phys. Rev. E 72 (6), 066705.CrossRefGoogle ScholarPubMed
Redlich, O. & Kwong, J.N.S. 1949 On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Chem. Rev. 44 (1), 233–244.CrossRefGoogle Scholar
Ren, Q. 2019 Enhancement of nanoparticle-phase change material melting performance using a sinusoidal heat pipe. Energy Convers. Manage. 180, 784–795.CrossRefGoogle Scholar
Rojas, R., Takaki, T. & Ohno, M. 2015 A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection. J.Comput. Phys. 298, 29–40.CrossRefGoogle Scholar
Rykov, V.A. 1975 A model kinetic equation for a gas with rotational degrees of freedom. Fluid Dyn. 10 (6), 959–966.CrossRefGoogle Scholar
Safari, H., Rahimian, M.H. & Krafczyk, M. 2014 Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method. Phys. Rev. E 90 (3), 033305.CrossRefGoogle ScholarPubMed
Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., Sugiyama, K. & Toschi, F. 2007 Generalized lattice Boltzmann method with multirange pseudopotential. Phys. Rev. E 75 (2), 026702.CrossRefGoogle ScholarPubMed
Sbragaglia, M. & Succi, S. 2005 Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions. Phys. Fluids 17 (9), 093602.CrossRefGoogle Scholar
Schweizer, M., Öttinger, H.C. & Savin, T. 2016 Nonequilibrium thermodynamics of an interface. Phys. Rev. E 93 (5), 052803.CrossRefGoogle ScholarPubMed
Shakhov, E.M. 1968 Generalization of the Krook kinetic relaxation equation. Fluid Dyn. 3 (5), 95–96.CrossRefGoogle Scholar
Shan, X. & Chen, H. 1993 Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47 (3), 1815–1819.CrossRefGoogle ScholarPubMed
Shan, X. & Chen, H. 1994 Simulation of nonideal gases and liquid–gas phase transitions by the lattice Boltzmann equation. Phys. Rev. E 49 (4), 2941–2948.CrossRefGoogle ScholarPubMed
Shan, X., Yuan, X. & Chen, H. 2006 Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation. J.Fluid Mech. 550, 413–441.CrossRefGoogle Scholar
Shi, Y. & Shan, X. 2021 A multiple-relaxation-time collision model for nonequilibrium flows. Phys. Fluids 33 (3), 037134.CrossRefGoogle Scholar
Shi, Y., Wu, L. & Shan, X. 2021 Accuracy of high-order lattice Boltzmann method for non-equilibrium gas flow. J.Fluid Mech. 907, A25.CrossRefGoogle Scholar
Sofonea, V., Biciuşcă, T., Busuioc, S., Ambruş, V.E., Gonnella, G. & Lamura, A. 2018 Corner-transport-upwind lattice Boltzmann model for bubble cavitation. Phys. Rev. E 97 (2), 023309.CrossRefGoogle ScholarPubMed
Sofonea, V., Lamura, A., Gonnella, G. & Cristea, A. 2004 Finite-difference lattice Boltzmann model with flux limiters for liquid–vapor systems. Phys. Rev. E 70 (4), 046702.CrossRefGoogle ScholarPubMed
Sofonea, V. & Sekerka, R.F. 2005 Diffuse-reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: evidence of temperature jump and slip velocity in microchannels. Phys. Rev. E 71 (6), 066709.CrossRefGoogle ScholarPubMed
Stanley, H.E. 1971 Phase Transitions and Critical Phenomena. Clarendon Press.Google Scholar
Struchtrup, H. 1997 The BGK-model with velocity-dependent collision frequency. Contin. Mech. Thermodyn. 9 (1), 23–31.CrossRefGoogle Scholar
Struchtrup, H. 2005 Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory. Springer.CrossRefGoogle Scholar
Struchtrup, H., Beckmann, A., Rana, A.S. & Frezzotti, A. 2017 Evaporation boundary conditions for the R13 equations of rarefied gas dynamics. Phys. Fluids 29 (9), 092004.CrossRefGoogle Scholar
Struchtrup, H. & Frezzotti, A. 2022 Twenty-six moment equations for the Enskog–Vlasov equation. J.Fluid Mech. 940, A40.CrossRefGoogle Scholar
Struchtrup, H. & Torrilhon, M. 2003 Regularization of Grad's 13 moment equations: derivation and linear analysis. Phys. Fluids 15 (9), 2668–2680.CrossRefGoogle Scholar
Su, X. & Lin, C. 2022 Nonequilibrium effects of reactive flow based on gas kinetic theory. Commun. Theor. Phys. 74 (3), 035604.CrossRefGoogle Scholar
Succi, S. 2001 The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press.Google Scholar
Succi, S. 2014 A note on the lattice Boltzmann versus finite-difference methods for the numerical solution of the Fisher's equation. Intl J. Mod. Phys. C 25 (01), 1340015.CrossRefGoogle Scholar
Succi, S. 2018 The Lattice Boltzmann Equation: For Complex States of Flowing Matter. Oxford University Press.CrossRefGoogle Scholar
Succi, S., Amati, G., Bonaccorso, F., Lauricella, M., Bernaschi, M., Montessori, A. & Tiribocchi, A. 2020 Toward exascale design of soft mesoscale materials. J.Comput. Sci. 46, 101175.CrossRefGoogle Scholar
Succi, S., Montessori, A., Lauricella, M., Tiribocchi, A. & Bonaccorso, F. 2021 Density functional kinetic theory for soft matter. In Proceedings of SIMAI 2020+21.Google Scholar
Sun, D., Pan, S., Han, Q. & Sun, B. 2016 a Numerical simulation of dendritic growth in directional solidification of binary alloys using a lattice Boltzmann scheme. Intl J. Heat Mass Transfer 103, 821–831.CrossRefGoogle Scholar
Sun, D., Zhu, M., Wang, J. & Sun, B. 2016 b Lattice Boltzmann modeling of bubble formation and dendritic growth in solidification of binary alloys. Intl J. Heat Mass Transfer 94, 474–487.CrossRefGoogle Scholar
Swift, M.R., Orlandini, E., Osborn, W.R. & Yeomans, J.M. 1996 Lattice Boltzmann simulations of liquid–gas and binary fluid systems. Phys. Rev. E 54 (5), 5041–5052.CrossRefGoogle ScholarPubMed
Swift, M.R., Osborn, W.R. & Yeomans, J.M. 1995 Lattice Boltzmann simulation of nonideal fluids. Phys. Rev. Lett. 75 (5), 830–833.CrossRefGoogle ScholarPubMed
Tavares, H.S., Biferale, L., Sbragaglia, M. & Mailybaev, A.A. 2021 Immiscible Rayleigh–Taylor turbulence using mesoscopic lattice Boltzmann algorithms. Phys. Rev. Fluids 6 (5), 054606.CrossRefGoogle Scholar
Tian, Y., et al. 2022 Artificial mitochondrion for fast latent heat storage: experimental study and lattice Boltzmann simulation. Energy 245, 123296.CrossRefGoogle Scholar
Torrilhon, M. 2016 Modeling nonequilibrium gas flow based on moment equations. Annu. Rev. Fluid Mech. 48, 429–458.CrossRefGoogle Scholar
Toschi, F. & Succi, S. 2005 Lattice Boltzmann method at finite Knudsen numbers. Europhys. Lett. 69 (4), 549.CrossRefGoogle Scholar
Vilar, J.M.G. & Rubi, J.M. 2001 Thermodynamics ‘beyond’ local equilibrium. Proc. Natl Acad. Sci. 98 (20), 11081–11084.CrossRefGoogle ScholarPubMed
Wagner, A.J. 2003 The origin of spurious velocities in lattice Boltzmann. Intl J. Mod. Phys. C 17 (1–2), 193–196.CrossRefGoogle Scholar
Wagner, A.J. 2006 Thermodynamic consistency of liquid–gas lattice Boltzmann simulations. Phys. Rev. E 74 (5), 056703.CrossRefGoogle ScholarPubMed
Wagner, A.J. & Pagonabarraga, I. 2002 Lees–Edwards boundary conditions for lattice Boltzmann. J.Stat. Phys. 107 (1), 521–537.CrossRefGoogle Scholar
Wagner, A.J., Wilson, L.M. & Cates, M.E. 2003 Role of inertia in two-dimensional deformation and breakdown of a droplet. Phys. Rev. E 68 (4), 045301.CrossRefGoogle Scholar
Wagner, A.J. & Yeomans, J.M. 1998 Breakdown of scale invariance in the coarsening of phase-separating binary fluids. Phys. Rev. Lett. 80 (7), 1429.CrossRefGoogle Scholar
Wang, H. 2017 a Numerical simulation for the solitary wave of Zakharov–Kuznetsov equation based on lattice Boltzmann method. Appl. Math. Model. 45, 1–13.CrossRefGoogle Scholar
Wang, H. 2017 b Solitary wave of the Korteweg–de Vries equation based on lattice Boltzmann model with three conservation laws. Adv. Space Res. 59 (1), 283–292.CrossRefGoogle Scholar
Wang, H. 2019 Numerical simulation for solitary wave of Klein–Gordon–Zakharov equation based on the lattice Boltzmann model. Comput. Maths Applics. 78 (12), 3941–3955.CrossRefGoogle Scholar
Wang, H. 2020 Numerical simulation for (3+1)D solitary wave of extended Zakharov–Kuznetsov equation in dusty plasma based on lattice Boltzmann method. Phys. Lett. A 384 (32), 126809.CrossRefGoogle Scholar
Wang, H., Li, X., Li, Y. & Geng, X. 2017 Simulation of phase separation with large component ratio for oil-in-water emulsion in ultrasound field. Ultrason. Sonochem. 36, 101–111.CrossRefGoogle ScholarPubMed
Wang, Y., Shu, C., Huang, H.B. & Teo, C.J. 2015 a Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio. J.Comput. Phys. 280, 404–423.CrossRefGoogle Scholar
Wang, Y., Shu, C. & Yang, L. 2015 b An improved multiphase lattice Boltzmann flux solver for three-dimensional flows with large density ratio and high Reynolds number. J.Comput. Phys. 302, 41–58.CrossRefGoogle Scholar
Wang, C., Xu, A., Zhang, G. & Li, Y. 2009 Simulating liquid–vapor phase separation under shear with lattice Boltzmann method. Sci. China, Ser. G 52 (9), 1337–1344.CrossRefGoogle Scholar
Watari, M. 2016 Is the lattice Boltzmann method applicable to rarefied gas flows? Comprehensive evaluation of the higher-order models. J.Fluids Engng 138 (1), 011202.CrossRefGoogle Scholar
Weeks, J.D. 1977 Structure and thermodynamics of the liquid–vapor interface. J.Chem. Phys. 67 (7), 3106–3121.CrossRefGoogle Scholar
Wei, Y, Li, Y., Wang, Z., Yang, H., Zhu, Z., Qian, Y. & Luo, K.H. 2022 Small-scale fluctuation and scaling law of mixing in three-dimensional rotating turbulent Rayleigh–Taylor instability. Phys. Rev. E 105 (1), 015103.CrossRefGoogle ScholarPubMed
Wen, B., Zhao, L., Qiu, W., Ye, Y. & Shan, X. 2020 Chemical-potential multiphase lattice Boltzmann method with superlarge density ratios. Phys. Rev. E 102 (1), 013303.CrossRefGoogle ScholarPubMed
Wen, B., Zhou, X., He, B., Zhang, C. & Fang, H. 2017 Chemical-potential-based lattice Boltzmann method for nonideal fluids. Phys. Rev. E 95 (6), 063305.CrossRefGoogle ScholarPubMed
Wöhrwag, M., Semprebon, C., Mazloomi Moqaddam, A., Karlin, I. & Kusumaatmaja, H. 2018 Ternary free-energy entropic lattice Boltzmann model with a high density ratio. Phys. Rev. Lett. 120 (23), 234501.CrossRefGoogle ScholarPubMed
Wu, J.L., Li, Z.H., Zhang, Z.B. & Peng, A.P. 2021 a On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm. J.Comput. Phys. 435, 109938.CrossRefGoogle Scholar
Wu, W., Liu, Q. & Wang, B. 2021 b Curved surface effect on high-speed droplet impingement. J.Fluid Mech. 909, A7.CrossRefGoogle Scholar
Xu, K. 2014 Direct Modeling for Computational Fluid Dynamics: Construction and Application of Unified Gas-Kinetic Schemes. World Scientific Publishing.Google Scholar
Xu, A., Chen, J., Song, J., Chen, D. & Chen, Z. 2021 a Progress of discrete Boltzmann study on multiphase complex flows. Acta Aerodyn. Sin. 39 (3), 138–169.Google Scholar
Xu, A., Gonnella, G. & Lamura, A. 2003 Phase-separating binary fluids under oscillatory shear. Phys. Rev. E 67 (5), 056105.CrossRefGoogle ScholarPubMed
Xu, A., Gonnella, G. & Lamura, A. 2004 Numerical study of the ordering properties of lamellar phase. Physica A 344 (3–4), 750–756.CrossRefGoogle Scholar
Xu, A., Shan, Y., Chen, F., Gan, Y. & Lin, C. 2021 b Progress of mesoscale modeling and investigation of combustion multi-phase flow. Acta Aeronaut. Astronaut. Sin. 42 (12), 625842.Google Scholar
Xu, A., Song, J., Chen, F., Xie, K. & Ying, Y. 2021 c Modeling and analysis methods for complex fields based on phase space. Chinese J. Comput. Phys. 38 (6), 631.Google Scholar
Xu, Y.Q., Wang, M.Y., Liu, Q.Y., Tang, X.Y. & Tian, F.B. 2018 b External force-induced focus pattern of a flexible filament in a viscous fluid. Appl. Math. Model. 53, 369–383.CrossRefGoogle Scholar
Xu, A.G., Zhang, G.C., Gan, Y.B., Chen, F. & Yu, X.J. 2012 Lattice Boltzmann modeling and simulation of compressible flows. Front. Phys. 7 (5), 582–600.CrossRefGoogle Scholar
Xu, A., Zhang, G. & Zhang, Y. 2018 a Discrete Boltzmann modeling of compressible flows. In Kinetic Theory, Chap. 02. (ed. G.Z. Kyzas & A.C. Mitropoulos). InTech.CrossRefGoogle Scholar
Yan, G. 2000 A lattice Boltzmann equation for waves. J.Comput. Phys. 161 (1), 61–69.Google Scholar
Yan, W., Cai, B., Liu, Y. & Fu, B. 2012 Effects of wall shear stress and its gradient on tumor cell adhesion in curved microvessels. Biomech. Model. Mechanobiol. 11 (5), 641–653.CrossRefGoogle ScholarPubMed
Yang, Z., Liu, S., Zhuo, C. & Zhong, C. 2022 b Free-energy-based discrete unified gas kinetic scheme for van der Waals fluid. Entropy 24 (9), 1202.CrossRefGoogle ScholarPubMed
Yang, Y., Shan, M., Kan, X., Shangguan, Y. & Han, Q. 2020 Thermodynamic of collapsing cavitation bubble investigated by pseudopotential and thermal MRT-LBM. Ultrason. Sonochem. 62, 104873.CrossRefGoogle ScholarPubMed
Yang, Y., Shan, M., Su, N., Kan, X., Shangguan, Y. & Han, Q. 2022 a Role of wall temperature on cavitation bubble collapse near a wall investigated using thermal lattice Boltzmann method. Intl Commun. Heat Mass Transfer 134, 105988.CrossRefGoogle Scholar
Yang, L.M., Shu, C., Yang, W.M., Chen, Z. & Dong, H. 2018 An improved discrete velocity method (DVM) for efficient simulation of flows in all flow regimes. Phys. Fluids 30 (6), 062005.CrossRefGoogle Scholar
Yang, Z., Zhong, C. & Zhuo, C. 2019 Phase-field method based on discrete unified gas-kinetic scheme for large-density-ratio two-phase flows. Phys. Rev. E 99 (4), 043302.CrossRefGoogle ScholarPubMed
Zang, D. 2020 Acoustic Levitation: From Physics to Applications. Springer Nature.CrossRefGoogle Scholar
Zang, D., Tarafdar, S., Tarasevich, Y.Y., Choudhury, M.D. & Dutta, T. 2019 Evaporation of a droplet: from physics to applications. Phys. Rep. 804, 1–56.CrossRefGoogle Scholar
Zarghami, A. & Van den Akker, H.E.A. 2017 Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method. Phys. Rev. E 95 (4), 043310.CrossRefGoogle ScholarPubMed
Zhang, R., He, X., Doolen, G. & Chen, S. 2001 Surface tension effects on two-dimensional two-phase Kelvin–Helmholtz instabilities. Adv. Water Res. 24 (3-4), 461–478.CrossRefGoogle Scholar
Zhang, R., Shan, X. & Chen, H. 2006 Efficient kinetic method for fluid simulation beyond the Navier–Stokes equation. Phys. Rev. E 74 (4), 046703.CrossRefGoogle ScholarPubMed
Zhang, Y., Xu, A., Chen, F., Lin, C. & Wei, Z.H. 2022 b Non-equilibrium characteristics of mass and heat transfers in the slip flow. AIP Adv. 12 (3), 035347.CrossRefGoogle Scholar
Zhang, Y., Xu, A., Zhang, G., Gan, Y., Chen, Z. & Succi, S. 2019 Entropy production in thermal phase separation: a kinetic-theory approach. Soft Matt. 15 (10), 2245–2259.CrossRefGoogle ScholarPubMed
Zhang, D., Xu, A., Zhang, Y., Gan, Y. & Li, Y. 2022 a Discrete Boltzmann modeling of high-speed compressible flows with various depths of non-equilibrium. Phys. Fluids 34, 086104.CrossRefGoogle Scholar
Zhang, D., Xu, A., Zhang, Y. & Li, Y. 2020 Two-fluid discrete Boltzmann model for compressible flows: based on ellipsoidal statistical Bhatnagar–Gross–Krook. Phys. Fluids 32 (12), 126110.CrossRefGoogle Scholar
Zhang, G., Xu, A., Zhang, D., Li, Y., Lai, H. & Hu, X. 2021 Delineation of the flow and mixing induced by Rayleigh–Taylor instability through tracers. Phys. Fluids 33 (7), 076105.CrossRefGoogle Scholar
Zhang, Y., Xu, A., Zhang, G., Zhu, C. & Lin, C. 2016 Kinetic modeling of detonation and effects of negative temperature coefficient. Combust. Flame 173, 483–492.CrossRefGoogle Scholar
Zhang, J. & Yan, G. 2010 Lattice Boltzmann model for the complex Ginzburg–Landau equation. Phys. Rev. E 81 (6), 066705.CrossRefGoogle ScholarPubMed
Zhang, J. & Yan, G. 2014 Three-dimensional lattice Boltzmann model for the complex Ginzburg–Landau equation. J.Sci. Comput. 60 (3), 660–683.CrossRefGoogle Scholar
Zhang, J., Yan, G. & Dong, Y. 2009 A new lattice Boltzmann model for the Laplace equation. Appl. Maths Comput. 215 (2), 539–547.CrossRefGoogle Scholar
Zheng, H.W., Shu, C. & Chew, Y.T. 2006 A lattice Boltzmann model for multiphase flows with large density ratio. J.Comput. Phys. 218 (1), 353–371.CrossRefGoogle Scholar