Kyle Lange

A Fully Implicit Characteristic-Based Algorithm for a One Dimensional Radio Frequency Glow Discharge Fluid Simulation

A Thesis Presented for the Master of Science in Computational Engineering Degree, The University of Tennessee at Chattanooga

Kyle Joseph Lange, August 2007

Abstract:
A fully implicit numerical scheme is developed to solve the fluid equations describing the dynamics of a radio frequency glow discharge on a one-dimensional mesh. The equations are cast in conservative form in order to extend the equations to multiple dimensions and to facilitate the implementation of characteristic-based upwind schemes. Results obtained from Roe’s flux-difference splitting, Steger-Warming flux-vector splitting, and van Leer flux-vector splitting are compared. The numerical algorithm is shown to be second order convergent in time and space. Simplifications of the algorithm are tested to investigate the effects on computational resources and robustness. Power computations for the bulk plasma are compared to previous results. Suggestions for improving the efficiency of the algorithm and extending the work to multiple dimensions are made.