Gas discharge modelling using the finite-element flux-corrected transport method

This thesis presents the development of a new numerical algorithm and its application to the solution of gas discharge problems. The algorithm uses finite-element (FE) analysis in conjunction with the flux-corrected transport (FCT) method and has the distinct advantage that it can study gas discharge phenomena in arbitrary geometries accurately and efficiently. The FE-FCT method is firstly presented in one dimension and its performance optimised by using the optimum diffusion. This is then used to describe the motion of electrons and ions in one dimension and coupled to Poisson's equation in two dimensions to create a new gas discharge algorithm. In order to test and verify the algorithm, numerical results are obtained for the formation of corona and streamers in a short needle-plane gap in air, which a.re compared with pre-existing finitedifference results, yielding very good agreement. Having validated the algorithm, it is then applied to the problem of corona development at radio frequencies (RF) , the pre-cursor of fully developed arcs in RF systems. RF corona discharges in a point-plane gap in air are investigated and the importance of different parameters is examined. The capabilities of the FE-FCT method are then exploited further by extending it in its two-dimensional form in cartesian and cylindrical co-ordinates. The new method is once more validated by comparing its performance with analytical expressions and a pre-existing FD-FCT code. Finally, the two dimensional FE-FCT method is coupled to Poisson's equation in order to study gas discharge problems in two dimensions. Primarily, the new algorithm is tested in cases where experimental and theoretical results exist, in order to evaluate its accuracy and potential for solving gas discharge problems and then it is used to give important information about fundamental processes. Results for the avalanche to streamer transition and propagation in parallel-plane electrodes in air are presented