Speeding Up Fluid Models for Gas Discharges by Implicit Treatment of the Electron Energy Source Term

Abstract

Numerical fluid models are widely used in gas discharge physics. A typical discharge model comprises continuity equations and drift–diffusion equations for reactive particle species, a balance equation for the electron energy, and Poisson's equation for the electric field. When this system of equations is integrated numerically with respect to time, the explicit evaluation of coupled quantities necessitates strong time step restrictions, resulting in an enormous slowdown of the calculation. The strongest time step restriction arises from an explicit treatment of the coupling between the charged particle transport and the space charge field. In order to circumvent this constraint several implicit and semi-implicit techniques have been developed. When one uses these techniques, however, the explicit handling of the dependence of electron energy source term on the electron mean energy becomes limiting for the time step. In this work we present a technique for the implicit treatment of the electron energy source term, based on linearization with respect to the electron mean energy. This approach makes it possible to increase the time step by several orders of magnitude, thus giving a tremendous speedup of the calculation. Test results are provided for some typical cases, covering a wide range of numerical conditions.