STOCHASTIC SIMULATION OF TRANSPORT PHENOMENA

In this paper, four examples are given to demonstrate how stochastic s imulations can be used as a method to obtain numerical solutions to tr ansport problems. The problems considered are two-dimensional heat con duction, mass diffusion with reaction, the start-up of Poiseuille flow , and Couette flow of a suspension of Hookean dumbbells. The first thr ee examples are standard problems with well-known analytic-solutions w hich can be used to verify the results of the stochastic simulation. T he fourth example combines a Brownian dynamics simulation for Hookean dumbbells, a crude model of a dilute polymer suspension, and a stochas tic simulation for the suspending, Newtonian fluid. These examples ill ustrate appropriate methods for handling source/sink terms and initial and boundary conditions. The stochastic simulation results compare we ll with the analytic solutions and other numerical solutions. The goal of this paper is to demonstrate the wide applicability of stochastic simulation as a numerical method for transport problems.