A two-dimensional, finite-element, flux-corrected transport algorithm for the solution of gas discharge problems

An improved finite-element flux-corrected transport (FE-FCT) scheme, which was demonstrated in one dimension by the authors, is now extended to two di mensions and applied to gas discharge problems. The low-order positive ripp le-free scheme, required to produce a FCT algorithm, is obtained by introdu cing diffusion to the high-order scheme (two-step Taylor-Galerkin). A self- adjusting variable diffusion coefficient is introduced, which reduces the h igh-order scheme to the equivalent of the upwind difference scheme, but wit hout the complexities of an upwind scheme in a finite-element setting. Resu lts are presented which show that the high-order scheme reduces to the equi valent of upwinding when the new diffusion coefficient is used. The propose d FCT scheme is shown to give similar results in comparison to a finite-dif ference time-split FCT code developed by Boris and Book. Finally, the new m ethod is applied for the first time to a streamer propagation problem in it s two-dimensional form.