An Improved Finite-Element Flux-Corrected Transport Algorithm

Abstract

An improved finite-element flux-corrected transport (FE-FCT) method for the numerical solution of hydrodynamic conservation equations is described, based on the method developed by Lohner and his collaborators to solve conservation equations in fluid mechanics, and its application is extended to gas discharge problems. The high- and low-order schemes used are the ones proposed by Lohner who adds diffusion to the high-order scheme by subtracting the lumped-mass matrix from the consistent-mass matrix to give the low-order scheme; the diffusion coefficient is adjusted globally. A variable diffusion coefficient is introduced; it is assumed to be constant in each element and is shown to transform the high-order solution to a scheme equivalent to an upwind scheme which has minimal diffusion but ensures positive results. This avoids the complexity of upwinding in FE, especially in two dimensions. It is also shown that the correct amount of “real” diffusion may be easily added to the algorithm when required, for example, for electrons. Results are presented which show that the high-order scheme reduces to the upwind difference scheme when the new diffusion is used. The proposed FCT scheme is shown to give similar results, in comparison with a fourth-order FD-FCT algorithm. Finally, the new method is applied to a streamer propagation problem in one dimension, and the results obtained are shown to agree well with previously published results.