A Lattice Boltzmann-Direct Forcing/Fictitious Domain Model for Brownian Particles in Fluctuating Fluids (Communications in Computational Physics, 2011)
The previously developed LB-DF/FD method derived from the lattice Boltzmannmethod and Direct Forcing/Fictitious Domain method is extended to deal with3D particle's Brownian motion. In the model the thermal fluctuations are introducedas random forces and torques acting on the Brownian particle. The hydrodynamic interactionis introduced by directly resolving the fluid motions. A sphere fluctuating ina cubic box with the periodic boundary is considered to validate the present model.By examining the velocity autocorrelation function (VCF) and rotational velocity autocorrelationfunction (RVCF), it has been found that in addition to the two relaxationtimes, the mass density ratio should be taken into consideration to check the accuracyand effectiveness of the present model. Furthermore, the fluctuation-dissipation theoremand equipartition theorem have been investigated for a single spherical particle.Finally, a Brownian particle trapped in a harmonic potential has been simulated tofurther demonstrate the ability of the LB-DF/FD model.