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Basic Lattice-Boltzmann (LB) MATLAB Code



10 Feb 2005 (Updated )

Implements LB BGK D2Q9.

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Simple, yet simplistic, Lattice Boltzmann (LB) MATLAB implementation. D2H9, BGK, omega = 1, laminar flow in a 2D channel used as benchmark. Requires Image Processing Toolbox.

The code is not optimized for memory nor for speed, i.e. not efficient at all. However, it is better than almost nothing (i.e. the present MATLAB situation at Feb 2005 ? as far as I know)
Optimization for memory should consider only dry locations.

Other free LB (FORTRAN, C, and Cpp) codes are available:

See the anb.f code at or the S.Succi code available from
See also D2Q9poi.f from Dieter Wolf-Gladrow and written by Kraft and Schultz t

See also the translation into C of the original Succi FORTAN code

See also lb2d.m (by Youngseuk Keehm) at

For LB benchmarking see:
and page 190-192 in: Lattice-gas cellular automata and lattice Boltzmann models: an introduction / Dieter A. Wolf-Gladrow. -. ISBN: 3540669736.

This code is written to be readable by the most, optimisation makes it less readable. It is mean to be of some help to students tackling LB for the first time. As usual no guarantee of bug free or proper functioning. in the hope that some of the many LB developers will make soon something better available to the MATLAB community? possibly 3D, possibly multi-phase / multi-component.

Suggestions: Rather than rating, please- makes available a better code than this, it is an easier task. The user should not be surprise by encountering instability by changing the parameters without a precise rational. I suggest reading the references that benchmark the LB BKG and follow the given examples in order to get a feeling of the sensitivity of the code to the different variables.

Required Products Image Processing Toolbox
MATLAB release MATLAB 7.1.0 (R14SP3)
Other requirements none
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Comments and Ratings (12)
08 Jul 2014 Arash

Arash (view profile)

I try to submit my own code when it's ready, and thanks for your effort and contribution :)

16 Aug 2011 mohammad pourtousi

please tell me how can i use b.c FOR INLET AND OUT LET for pipe

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28 Feb 2011 emn

emn (view profile)

i have a problem with convection diffusion code i must vary the peclet number from 0.1 to 10^5 and i cant find a solution to this using LBM.
Please how can I do this or if there is any code available for that

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01 Jul 2010 rahul sharma

hiii..plz tell me how to write a code for sound propagation using cellular automata.... i want to simulate longitudinal waves and transverse waves....

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01 Sep 2008 sung yi


31 Dec 2007 vinu varghese

please let me know how can i simualate efficiently the Couette flow using LBM.Or if there is any code available for that

18 Dec 2007 gianni schena

mr cao xudong (
generic notices of possible mistakes are of little help for the matlab community
if you point out precisely the problem we will be most than happy to tackle the problem (if any) and correct the contribution if necessary . Thank you for the cooperation

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03 Dec 2007 cao xudong

there is some mistake in the boundery condition and initialization

25 Oct 2006 mehr ashwin

Please make code for "multiple relaxation time LBE model (Humieres,2002)" available.

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02 May 2006 gianni schena

see also this new (2006) http

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24 May 2005 houat samir  
21 Feb 2005 gianni schena

ux=ux./rho; uy=uy./rho; uxsq=ux.^2; uysq=uy.^2; usq=uxsq+uysq; %

% BKG Equilibrium distribution
% smart way to avoid the for loop .. eg. ic=5
f(ija+NxM*(5-1))= rt2(ija) .*(1 +f1*(+ux(ija)+uy(ija)) +f2*(+ux(ija)+uy(ija)).^2 -f3.*usq(ija));
%and the alike for the other values of ic up to ic=9
f(ija+NxM*(9-1))= rt0(ija) .*(1 - f3*usq(ija));

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