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Published: 7 July 2024

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1

Mohamad, A. A. Lattice Boltzmann Method. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-455-5.

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2

Mohamad, A. A. Lattice Boltzmann Method. London: Springer London, 2019. http://dx.doi.org/10.1007/978-1-4471-7423-3.

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3

Krüger, Timm, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, Goncalo Silva, and Erlend Magnus Viggen. The Lattice Boltzmann Method. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-44649-3.

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4

Luo, Li-Shi. Applications of the Lattice Boltzmann method to complex and turbulent flows. Hampton, Va: ICASE, NASA Langley Research Center, 2002.

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5

Mohamad, A. A. Lattice Boltzmann method: Fundamentals and engineering applications with computer codes / A. A. Mohamad. London: Springer, 2011.

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6

Lallemand, Pierre. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2000.

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7

Han, Mengtao, and Ryozo Ooka. Large-Eddy Simulation Based on the Lattice Boltzmann Method for Built Environment Problems. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-1264-3.

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8

Yeh, Chou, and Langley Research Center, eds. On higher order dynamics in lattice-based models using Chapman-Enskog method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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9

Succi, Sauro. Entropic Lattice Boltzmann. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0021.

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The LB with enhanced collisions opened the way to the top-down design of LB schemes, with major gains in flexibility and computational efficiency. However, compliance with the second principle was swept under the carpet in the process, with detrimental effects on the numerical stability of the method. It is quite fortunate that, albeit forgotten, the above compliance did not get lost in the top-down procedure. Entropic LB schemes, the object of the present chapter, explain the whys and hows of this nice smile of Lady Luck.

10

Succi, Sauro. Lattice Boltzmann Models for Microflows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0029.

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The Lattice Boltzmann method was originally devised as a computational alternative for the simulation of macroscopic flows, as described by the Navier–Stokes equations of continuum mechanics. In many respects, this still is the main place where it belongs today. Yet, in the past decade, LB has made proof of a largely unanticipated versatility across a broad spectrum of scales, from fully developed turbulence, to microfluidics, all the way down to nanoscale flows. Even though no systematic analogue of the Chapman–Enskog asymptotics is available in this beyond-hydro region (no guarantee), the fact remains that, with due extensions of the basic scheme, the LB has proven capable of providing several valuable insights into the physics of flows at micro- and nano-scales. This does not mean that LBE can solve the actual Boltzmann equation or replace Molecular Dynamics, but simply that it can provide useful insights into some flow problems which cannot be described within the realm of the Navier–Stokes equations of continuum mechanics. This Chapter provides a cursory view of this fast-growing front of modern LB research.

11

Succi, Sauro. Lattice Boltzmann Models without Underlying Boolean Microdynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0013.

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Chapter 12 showed how to circumvent two major stumbling blocks of the LGCA approach: statistical noise and exponential complexity of the collision rule. Yet, the ensuing LB still remains connected to low Reynolds flows, due to the low collisionality of the underlying LGCA rules. The high-viscosity barrier was broken just a few months later, when it was realized how to devise LB models top-down, i.e., based on the macroscopic hydrodynamic target, rather than bottom-up, from underlying microdynamics. Most importantly, besides breaking the low-Reynolds barrier, the top-down approach has proven very influential for many subsequent developments of the LB method to this day.

12

Succi, Sauro. Lattice Boltzmann for Turbulence Modeling. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0024.

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This chapter introduces the main ideas behind the application of LBE methods to the problem of turbulence modeling, namely the simulation of flows which contain scales of motion too small to be resolved on present-day and foreseeable future computers. Many real-life flows of practical interest exhibit Reynolds numbers far too high to be directly simulated in full resolution on present-day computers and arguably for many years to come. This raises the challenge of predicting the behavior of highly turbulent flows without directly simulating all scales of motion which take part to turbulence dynamics, but only those that fall within the computer resolution at hand.

13

Succi, Sauro. Lattice Boltzmann for Turbulent Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0020.

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This chapter presents the main ideas behind the application of LB methods to the simulation of turbulent flows. The attention is restricted to the case of direct numerical simulation, in which all scales of motion within the grid resolution are retained in the simulation. Turbulence modeling, in which the effect of unresolved scales on the resolved ones is taken into account by various forms of modeling, will be treated in a subsequent chapter.

14

An Introduction to Lattice Boltzmann Method. World Scientific, 2021. http://dx.doi.org/10.1142/12375.

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15

Krüger, Timm, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, and Goncalo Silva. Lattice Boltzmann Method: Principles and Practice. Springer International Publishing AG, 2016.

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16

Theory of the lattice Boltzmann method: Lattice Boltzmann models for non-ideal gases. Hampton, VA: ICASE, NASA Langley Research Center, 2001.

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17

Succi, Sauro. Out of Legoland: Geoflexible Lattice Boltzmann Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0023.

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The LBEs discussed to this point lag behind “best in class” Computational Fluid Dynamics (CFD) methods for the simulation of fluid flows in realistically complicated geometries, such as those presented by most industrial devices. This traces back to the constraint of working along the light-cones of a uniform spacetime. Various methods have been proposed to remedy this unsatisfactory state of affairs. Among others, a natural strategy is to acquire geometrical flexibility from well-established techniques which can afford it, namely Finite Volumes (FV), Finite Differences (FD) and Finite Elements (FE). Alternatively, one can stick to the cartesian geometry of standard LB, and work at progressive levels of local grid refinement. This Chapter presents the general ideas being both strategies.

18

Krüger, Timm, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, Goncalo Silva, and Erlend Magnus Viggen. The Lattice Boltzmann Method: Principles and Practice. Springer, 2018.

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19

Krüger, Timm, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, Goncalo Silva, and Erlend Magnus Viggen. The Lattice Boltzmann Method: Principles and Practice. Springer, 2016.

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20

Lattice Boltzmann Method And Its Applications In Engineering. World Scientific Publishing Co Pte Ltd, 2013.

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21

Succi, Sauro. The Lattice Boltzmann Equation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.001.0001.

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Over the past near three decades, the Lattice Boltzmann method has gained a prominent role as an efficient computational method for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales, from fully developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic subnuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this book presents a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines, such as statistical physics, material science, soft matter and biology. This includes recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, the book also presents the extension of the Lattice Boltzmann method to quantum and relativistic fluids, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as quark-gluon plasmas and electron flows in graphene. It is hoped that this book may provide a source information and possibly inspiration to a broad audience of scientists dealing with the physics of classical and quantum flowing matter across many scales of motion.

22

Yu, Dazhi. Viscous flow computations with the lattice Boltzmann equation method. 2002.

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23

Mohamad, A. A. Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes. Springer London, Limited, 2014.

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24

National Aeronautics and Space Administration (NASA) Staff. Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry. Independently Published, 2018.

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25

Mohamad, A. A. Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes. Springer, 2011.

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26

Mohamad, A. A. Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes. Springer, 2019.

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27

National Aeronautics and Space Administration (NASA) Staff. Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows. Independently Published, 2018.

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28

Inamuro, Takaji, Kosuke (Mathematician) Suzuki, and Masato Yoshino. Introduction to Lattice Boltzmann Method: A Numerical Method for Complex Boundary and Moving Boundary Flows. World Scientific Publishing Co Pte Ltd, 2022.

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29

National Aeronautics and Space Administration (NASA) Staff. Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability. Independently Published, 2018.

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30

On higher order dynamics in lattice-based models using Chapman-Enskog method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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31

Succi, Sauro. LB for Flows with Suspended Objects: Fluid–Solid Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0031.

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In the recent years the theory of the fluctuating LB, as it was proposed and developed by A.J.C. Ladd in the early 90s, has undergone major developments, both at the level of theoretical foundations and practical implementation. This Chapter provides a cursory view of such developments, with special focus on the general formulation of fluid–solid interactions within the Lattice Boltzmann formalism. Clearly, the rheological behavior of these suspensions is highly accepted by the way the suspended particles interact with the fluid and among themselves. From the mathematical and computational standpoint, this configures a technically thick issue, namely the treatment of fluid-solid moving boundaries, in a more macroscopic-oriented context also known as fluid-structure interactions (FSI). In the sequel, a description of a number of methods which have been developed to include FSI within the LB formalism, is presented. In particular, the case of rigid and deformable bodies, both vital to many applications in science and engineering, shall be covered

32

Allen, Michael P., and Dominic J. Tildesley. Mesoscale methods. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803195.003.0012.

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Coarse-graining is an increasingly commonplace approach to study, as economically as possible, large-scale, and long-time phenomena. This chapter covers the main methods. Brownian and Langevin dynamics are introduced, with practical details of the solution of the modified equations of motion. Several techniques which aim to bridge the gap to the hydrodynamic regime are described: these include dissipative particle dynamics, multiparticle collision dynamics, and the lattice Boltzmann method. Several examples of program code are provided. In the last part of the chapter, the derivation of a coarse-grained potential from an atomistic one is considered using force-matching and structure-matching, and the limitations of these approaches are discussed.