Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-12-20
Physics
Condensed Matter
Statistical Mechanics
21 pages, 6 figures, submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.73.066707
We propose a discrete lattice version of the Fokker-Planck kinetic equation along lines similar to the Lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension $D$. A generalized Hermite-Gauss procedure is used to construct a discretized kinetic equation and a Chapman-Enskog expansion is applied to adapt the scheme so as to correctly reproduce the macroscopic continuum equations. The stability of the algorithm with respect to the finite time-step $\Delta t$ is characterized by the eigenvalues of the collision matrix. A heuristic second-order algorithm in $\Delta t$ is applied to investigate the time evolution of the distribution function of simple model systems, and compared to known analytical solutions. Preliminary investigations of sedimenting Brownian particles subjected to an orthogonal centrifugal force illustrate the numerical efficiency of the Lattice-Fokker-Planck algorithm to simulate non-trivial situations. Interactions between Brownian particles may be accounted for by adding a standard BGK collision operator to the discretized Fokker-Planck kernel.
Hansen Jean-Pierre
Melchionna Simone
Moroni Daniele
Rotenberg Benjamin
Succi Sauro
No associations
LandOfFree
Solving the Fokker-Planck kinetic equation on a lattice 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 Solving the Fokker-Planck kinetic equation on a lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solving the Fokker-Planck kinetic equation on a lattice will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-661685