Physics Department, Faculty of Sciences, University of Isfahan, Isfahan, I.R. Iran
Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulations. Particles’ trajectories for an ensemble of 1000 particles were calculated and compiled by Lagrangian approach. Numerical simulation in cartesian coordinate were validated by exact solution of Einstein and good agreement was observed. Moreover, strong convergence of proposed method has been considered. The approximated scheme has strong order of convergence, 1.5. Langevin equations in cylindrical coordinate were also considered as stochastic differential equations (SDE) and in different SDE calculus were solved numerically by validated numerical method. A novel approach to simulating the Brownian motion as the Gaussian white noise is presented in cylindrical coordinates. Obtained results for different SDEs calculus were compared and suggested that there are no considerable differences between Ito and Stratonovich approaches in two phase flow systems.