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Basic Lattice-Boltzmann (LB) MATLAB Code

version (5.7 KB) by gianni schena
Implements LB BGK D2Q9.


Updated 14 Nov 2005

No License

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.

Cite As

gianni schena (2020). Basic Lattice-Boltzmann (LB) MATLAB Code (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (14)

Check out my lastest framework for benchmark functions using python (numpy).


does anyone have the lb2d.m (by Youngseuk Keehm) matlab code?

your help would be highly appreciated


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

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


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

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

sung yi


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

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

cao xudong

there is some mistake in the boundery condition and initialization

mehr ashwin

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

gianni schena

houat samir

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));


improves an earlier code and allows simulation of porous systems in 2D

MATLAB Release Compatibility
Created with R14SP3
Compatible with any release
Platform Compatibility
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