An Particle Tracing Scheme for Fokker-Planck Equation in Finite Analytic/Monte Carlo Methods

Fokker-Planck equation for Stochastic system with whitenoise is reduced to velocity state vector, and the analytic solution of thereduced Fokker-Planck equation is obtained. The hybrid scheme in FiniteAnalytic/Monte Carlo methods is developed to simulate constant parameterscomplete Fokker-Planck equation and complete Fokker-Planck equation withvariable $F(X)$. It is shown that the results obtained from the numericalalgorthm are in good agrement with the analytic solutions, and that thesimulating PDF is smoothed when calculated particles number is 10$^{5}$, andthe simulating average moments are about to analytic solutions whencalculated particles number is 300. This work described here is first partof a long-term study in pursuit of a new simulating scheme for two-phaseflows.