Stochastic Simulation of Transport Phenomena

In this paper, four examples are given to demonstrate how stochastic simulations can be used as a method to obtain numerical solutions to transport problems. The problems considered are two-dimensional heat conduction, mass diffusion with reaction, the start-up of Poiseuille flow, and Couette flow of a suspension of Hookean dumbbells. The first three examples are standard problems with well-known analytic solutions which can be used to verify the results of the stochastic simulation. The fourth example combines a Brownian dynamics simulation for Hookean dumbbells, a crude model of a dilute polymer suspension, and a stochastic simulation for the suspending, Newtonian fluid. These examples illustrate appropriate methods for handling source/sink terms and initial and boundary conditions. The stochastic simulation results compare well 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.