Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2007-07-11
Physics
Condensed Matter
Soft Condensed Matter
Submitted to Physical Review E-11 pages Corrected Author(s) field on submittal form
Scientific paper
10.1103/PhysRevE.76.036704
We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each velocity direction occupied by many particles. We show that the most probable state of this model corresponds to the usual equilibrium distribution of the lattice Boltzmann equation. Thermal fluctuations about this equilibrium are controlled by the mean number of particles at a lattice site. Stochastic collision rules are described by a Monte Carlo process satisfying detailed balance. This allows for a straightforward derivation of discrete Langevin equations for the fluctuating modes. It is shown that all non-conserved modes should be thermalized, as first pointed out by Adhikari et al.; any other choice violates the condition of detailed balance. A Chapman-Enskog analysis is used to derive the equations of fluctuating hydrodynamics on large length and time scales; the level of fluctuations is shown to be thermodynamically consistent with the equation of state of an isothermal, ideal gas. We believe this formalism will be useful in developing new algorithms for thermal and multiphase flows.
Duenweg Burkhard
Ladd Anthony J. C.
Schiller Ulf D.
No associations
LandOfFree
Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-434777