  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.
