Brownian dynamics simulation of very small particles: Point source in uniform flow

We report Brownian dynamics simulations for the steady expansion of an axisymmetric jet of noninteracting particles injected from a point source into a backgroud gas with uniform temperature and velocity fields. Due to the nonequilibrium nature of the initial conditions, this problem may not be solved by application of the diffusion equation. Results are presented over the entire flow filed for particle density and velocity as well as all nonzero components of the particle temperature tensor. We compare the results to an exact solution for the same problem and the agreement is excellent. The simulations appear to converge to the exact solution as 1N∗ in the case of the velocity and density, and as 1√N∗ in the case of temperatures, where N∗ represents the number of trajectories simulated. To our knowledge, this is the first such nonequilibrium simulation to report the particle phase property fields, including the temperature tensor elements (which are more difficult to measure since they are related to small differences between primary properties). Further, we derive and present the correct (although nonintuitive) way to average quantities sampled at a constant axial position along the flow in such problems. Remarkably, these simulations are within the power of modern microcomputers, if overnight runs are used.