http://www.cnr.it/ontology/cnr/individuo/prodotto/ID167388
Solving the Fokker-Planck kinetic equation on a lattice (Articolo in rivista)
- Type
- Label
- Solving the Fokker-Planck kinetic equation on a lattice (Articolo in rivista) (literal)
- Anno
- 2006-01-01T00:00:00+01:00 (literal)
- Alternative label
Moroni, D; Rotenberg, B; Hansen, JP; Succi, S; Melchionna, S (2006)
Solving the Fokker-Planck kinetic equation on a lattice
(literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
- Moroni, D; Rotenberg, B; Hansen, JP; Succi, S; Melchionna, S (literal)
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- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
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- ISI Web of Science (WOS) (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- Univ Cambridge, Dept Chem, Cambridge CB2 1EW, England; Univ Paris 06, UMR 7612, CNRS, Lab Liquides Ion & Interfaces Chargee, F-75005 Paris, France; CNR, Ist Applicaz Calcolo M Picone, I-00161 Rome, Italy; Univ Roma La Sapienza, INFM, SOFT, Dept Phys, I-00185 Rome, Italy (literal)
- Titolo
- Solving the Fokker-Planck kinetic equation on a lattice (literal)
- Abstract
- We propose a discrete lattice version of the Fokker-Planck kinetic equation in close analogy with 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 linear 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 nontrivial situations. Interactions between Brownian particles may be accounted for by adding a standard Bhatnagar-Gross-Krook collision operator to the discretized Fokker-Planck kernel. (literal)
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