FINITE-ELEMENT METHOD FOR CONSERVATION EQUATIONS IN ELECTRICAL GAS-DISCHARGE AREAS

A powerful finite element method for numerical solution of hydrodynami c conservation equations of electrons and ions, including drift, diffu sion, and source terms, is proposed and applied in the area of electri cal gas discharges dominated by space charge effects and having steep variation of charge carrier densities. This numerical method, having a quite good conservative property and valid also for non-uniform mesh case, is able to take properly into account the possible discontinuiti es in space and/or time variation of electron and ion densities. Compa risons with an implicit finite difference scheme are first undertaken in the case of a standard problem of propagation of rectangular and Ga ussian initial waves without source term and with or without diffusion . Then, in the case of real discharges between two plane parallel elec trodes, hydrodynamic equations for charge carrier conservation coupled to Poisson equation have been solved. This has been undertaken to sho w the ability of the present numerical method to treat the classical d ischarges dominated by space charge effects such as the cathodic regio n of usual glow discharge in Ar and the propagation of ionizing waves in high pressure N2 discharge under overvoltage stress. (C) 1994 Acade mic Press, Inc.