PIC-FE and FCT-FE numerical simulation of two-dimensional electroconvection: Comparison of the results

The two-dimensional electroconvection between two plates has been studied from the theoretical and numerical point of view. However, the stability of the finite amplitude solution is an open theoretical problem. Here 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 is not always stable.