Commun. Comput. Phys., 9 (2011), pp. 959-973.

A Lattice Boltzmann-Direct Forcing/Fictitious Domain Model for Brownian Particles in Fluctuating Fluids

Deming Nie 1, Jianzhong Lin 1*

1 State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China; and College of Metrology and Technology Engineering, China Jiliang University, Hangzhou 310018, China.

Received 18 November 2009; Accepted (in revised version) 30 June 2010
Available online 2 November 2010


The previously developed LB-DF/FD method derived from the lattice Boltzmann method and Direct Forcing/Fictitious Domain method is extended to deal with 3D particle's Brownian motion. In the model the thermal fluctuations are introduced as random forces and torques acting on the Brownian particle. The hydrodynamic interaction is introduced by directly resolving the fluid motions. A sphere fluctuating in a cubic box with the periodic boundary is considered to validate the present model. By examining the velocity autocorrelation function (VCF) and rotational velocity autocorrelation function (RVCF), it has been found that in addition to the two relaxation times, the mass density ratio should be taken into consideration to check the accuracy and effectiveness of the present model. Furthermore, the fluctuation-dissipation theorem and equipartition theorem have been investigated for a single spherical particle. Finally, a Brownian particle trapped in a harmonic potential has been simulated to further demonstrate the ability of the LB-DF/FD model.

AMS subject classifications: 68U20, 76T20, 76M28, 82B80

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Key words: Lattice Boltzmann method, fictitious domain, Brownian motion.

*Corresponding author.
Email: (D. M. Nie),, (J. Z. Lin)

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