Abstract
An improved finite-element flux-corrected transport (FE-FCT)scheme, which was demonstrated in one dimension by the authors, is nowextended to two dimensions and applied to gas discharge problems. Thelow-order positive ripple-free scheme, required to produce a FCTalgorithm, is obtained by introducing diffusion to the high-orderscheme (two-step Taylor-Galerkin). A self-adjusting variable diffusioncoefficient is introduced, which reduces the high-order scheme to theequivalent of the upwind difference scheme, but without the complexities of anupwind scheme in a finite-element setting. Results are presented which showthat the high-order scheme reduces to the equivalent of upwinding when the newdiffusion coefficient is used. The proposed FCT scheme is shown to givesimilar results in comparison to a finite-difference time-split FCT codedeveloped by Boris and Book. Finally, the new method is applied for the firsttime to a streamer propagation problem in its two-dimensional form.
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