Fokker-Planck方程有限解析／Monte Carlo数值模拟方法  

A PARTICLE TRACING SCHEME FOR FOKKER-PLANCK EQUATION IN FINITE ANALYTIC/MONTE CARLO METHODS

作　　者：徐江荣[1] 周俊虎[2] 张平[1] 岑可法[2] 

机构地区：[1]杭州电子科技大学应用物理系,杭州310018 [2]浙江大学热能工程研究所,杭州310027

出　　处：《力学学报》2006年第1期73-78,共6页Chinese Journal of Theoretical and Applied Mechanics

基　　金：浙江省自然科学基金(Y105028)教育部跨世纪优秀人才培养计划(2002(48))资助项目.~~

摘　　要：对白噪声驱动随机系统的Fokker-Planck方程进行约化,求得约化方程的解析解,使用局部解析解和 Monte Carlo结合方法求解常系数Fokker-Planck方程,并与常系数Eokker-Planck方程的精确解进行对比, 之后求解了变驱动力系统的行为．数值模拟结果表明,有限解析／Monte Carlo结合的方法,能成功求解-维 Fokker-Planck方程,求解粒子数为105个,能获得十分光滑的PDF分布曲线,计算颗粒在300个时,就能获得较好的均值．其研究为两相湍流PDF模型新计算方法研究提供基础．Fokker-Planck equation for Stochastic system with white noise is reduced to velocity state vector, and the analytic solution of the reduced Fokker-Planck equation is obtained. The hybrid scheme in Finite Analytic/Monte Carlo methods is developed to simulate constant parameters complete Fokker-Planck equation and complete Fokker-Planck equation with variable F（X）. It is shown that the results obtained from the numerical algorthm are in good agrement with the analytic solutions, and that the simulating PDF is smoothed when calculated particles number is 10^5, and the simulating average moments are about to analytic solutions when calculated particles number is 300. This work described here is first part of a long-term study in pursuit of a new simulating scheme for two-phase flows.

关 键 词：FOKKER-PLANCK方程 MONTE CARLO方法 数值计算 两相流动 

分 类 号：TK121[动力工程及工程热物理—工程热物理]