| This thesis develops and applies computational tools describing the breakdown of a Dielectric Barrier Discharge (DBD) at high pressure---around atmospheric pressure. The computational schemes proposed here explicitly make use of the real underlying physics, in cases where standard numerical schemes are likely to fail. The errors which inevitably accompany finite differences and similar methods can dominate the solutions obtained. Emphasis is put on ensuring that the simulation captures the real physical behavior. Different schemes were developed and compared. First, a kinetic simulation of gas breakdown was implemented. Second, fluid simulations of the same phenomenon were set up, using rates and transport parameters found from the kinetic simulations. Accurate 'propagator' methods for solving drift-diffusion problems numerically were developed, which permit the fluid model to be used over a wide range of the time step and the mesh size. Various fluid models were examined and compared. Accurate models of breakdown preferably embody energy conservation and are Lagrangian; but it was discovered that such schemes often need a mesh size and time step which are prohibitively small. The results of the fluid simulations suggested a simplified, 'capacitor' model of the breakdown, which captures the same physics as the fluid models but which is much more efficient and prevents numerical diffusion. The TDCM was extended to two spatial dimensions. To avoid spurious ionization in the TDCM, the threshold density (a minimum density to ensure reaching the final density within a capacitor) was introduced in a cell only when the time reached the time that particles can physically drift into the capacitor. Otherwise density was not added. Density can be injected both along the axes and diagonally depending on the direction of the total electric field. One of the aims of this study is to understand the formation of the plasma 'plume' at both ends of the capillary discharge. The simulation results partially confirmed that the plume was caused by the parallel field pulling electrons to the ends of the capillary. However, a transverse field is also essential for breakdown to proceed in the presence of residual electrons in that area. |
