Lattice Boltzmann Method for Computational Fluid Dynamics

This article provides a concise survey of the lattice Boltzmann equation: its mathematical theory and its capabilities for applications in computational fluid dynamics (CFD). The lattice Boltzmann method stems from the Boltzmann equation, and thus differentiates from any conventional method for CFD based on direct discretizations of the Navier–Stokes equations. The lattice Boltzmann method is formulated for near incompressible flows. We will show some examples to demonstrate the state of the art and capabilities of the lattice Boltzmann method. The examples include direct numerical simulations of decaying homogeneous turbulence, large eddy simulations of flows past a sphere, suspensions in fluid, a droplet moving on a surface, and multi-component flows through porous media. The chapter is concluded with an outlook of future work. Keywords: Lattice Boltzmann equation; incompressible flows; DNS; LES; Suspensions in fluid; multi-component flows; complex flows through porous media

[1]  P. Lallemand,et al.  Momentum transfer of a Boltzmann-lattice fluid with boundaries , 2001 .

[2]  Pietro Asinari,et al.  A consistent lattice Boltzmann equation with baroclinic coupling for mixtures , 2008, J. Comput. Phys..

[3]  A. Ladd.  Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

[4]  P. Lallemand,et al.  Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Pierre Sagaut,et al.  Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics , 2009, J. Comput. Phys..

[6]  E. Achenbach,et al.  Experiments on the flow past spheres at very high Reynolds numbers , 1972, Journal of Fluid Mechanics.

[7]  Luo Li-Shi,et al.  Theory of the lattice Boltzmann method: Lattice Boltzmann models for non-ideal gases , 2001 .

[8]  L. Luo,et al.  Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation , 1997 .

[9]  Daniel H. Rothman,et al.  Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics , 1997 .

[10]  G. Constantinescu,et al.  Numerical investigations of flow over a sphere in the subcritical and supercritical regimes , 2004 .

[11]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[12]  Dominique d'Humières,et al.  Multireflection boundary conditions for lattice Boltzmann models. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[14]  A. Ladd,et al.  Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  M. Krafczyk,et al.  An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations , 2006 .

[17]  W. Shyy,et al.  Viscous flow computations with the method of lattice Boltzmann equation , 2003 .

[18]  Yan Peng,et al.  Comparison of the lattice Boltzmann and pseudo-spectral methods for decaying turbulence: Low-order statistics , 2010 .

[19]  Maxime Nicolas,et al.  2003 Francois Frankiel Award: Experimental study of gravity-driven dense suspension jets , 2002 .

[20]  Jonas Tölke,et al.  Lattice Boltzmann simulations of binary fluid flow through porous media , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[21]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  Manfred Krafczyk,et al.  LARGE-EDDY SIMULATIONS WITH A MULTIPLE-RELAXATION-TIME LBE MODEL , 2003 .

[23]  Andre Peters,et al.  Prediction of capillary hysteresis in a porous material using lattice-Boltzmann methods and comparison to experimental data and a morphological pore network model , 2008 .

[24]  Sharath S. Girimaji,et al.  LES of turbulent square jet flow using an MRT lattice Boltzmann model , 2006 .

[25]  K. L. Goin,et al.  Subsonic Drag of Spheres at Reynolds Numbers from 200 to 10,000 , 1968 .

[26]  M. Junk,et al.  Asymptotic analysis of the lattice Boltzmann equation , 2005 .

[27]  A. Ladd.  Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results , 1993, Journal of Fluid Mechanics.