An Implicit Flux-Corrected Transport Algorithm Used for Gas Discharge Calculations

An implicit flux-corrected transport (FCT) and diffusion algorithm was developed and used in many gas discharge calculations. Such calculations require the use of a fine mesh where the electric field changes rapidly; that is, near electrodes or in a streamer front. If diffusion is included using an explicit method, then the von Neumann stability condition severely limits the time-step that can be used; however, this limitation does not apply to implicit methods. Further, for gas discharge calculations including space-charge effects, it is necessary to solve the continuity equations with no negative number densities nor point-by-point oscillation in the number density. This is because the electron number densities are finely balanced with the ion number densities to determine the space-charge distribution and hence the electric field which drives the motion of the particles. An efficient way to solve the particle transport equation, with the required properties, is to use FCT. The most accurate form of FCT developed by the author is implicit fourth-order FCT; hence, the method presented incorporates implicit diffusion into the implicit fourth-order FCT scheme to produce a robust algorithm that has been successfully used in many calculations.