Computational methods for long mean free path problems

This document describes work being done on particle transport in long mean free path environments. Two non statistical computational models are developed based on the method of propagators, which can have significant advantages in accuracy and efficiency over other methods. The first model has been developed primarily for charged particle transport and the second primarily for neutral particle transport. Both models are intended for application to transport in complex geometry using irregular meshes. The transport model for charged particles was inspired by the notion of obtaining a simulation that could handle complex geometry and resolve the bulk and sheath characteristics of a discharge, in a reasonable amount of computation time. The charged particle transport model has been applied in a self-consistent manner to the ion motion in a low density inductively coupled discharge. The electrons were assumed to have a Boltzmann density distribution for the computation of the electric field. This work assumes cylindrical geometry and focuses on charge exchange collisions as the primary ion collisional effect that takes place in the discharge. The results are compared to fluid simulations. The neutral transport model was constructed to solve the steady state Boltzmann equation on 3-D arbitrary irregular meshes. The neutral transport model was developed with the intent of investigating gas glow on the scale of micro-electrical-mechanical systems (MEMS), and is meant for tracking multiple species. The advantage of these methods is that the step size is determined by the mean free path of the particles rather than the mesh employed in the simulation.