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.