Numerical study of the time evolution of finite amplitude electroconvection between two plates using PIC-FE and FCT-FE

We study the two-dimensional electroconvection between two plates from the theoretical and numerical point of view. We use two sets of numerical techniques to analyze this problem. On one hand, Particle-in-Cell techniques for simulating the charge distribution combined with Finite Elements for computing the velocity and electrical fields. On the other hand, Flux Corrected Transport for the charge and Finite Elements for the fields. We perform numerical simulations both for weak and strong injection beyond the linear stability threshold. The results seem to indicate that the one-roll finite amplitude solution assumed in previous both linear and non-linear stability analysis is not always stable.