The simulation of corona discharges usually requires an excessive amount of time. The objective of this work is therefore to reduce the CPU time of corona discharges. The profound disparity between physical time scales in a gas discharge renders explicit time integration impractical in large time scale applications, for example in flow controls. We propose an implicit time strategy in the scope of the Local Field Approximation plasma model. We investigate some algorithms to solve the discretized plasma model, which are adapted to take into consideration a constraint on the electron density. The constraint is introduced to compensate for unaccounted sources of electrons; it is expressed by a minimum/floor density imposed on the electrons. Therefore, simplified plasma models can be employed for discharge simulations, for instance a four-specie, four-reaction model is used in this article. The investigation is done on a one-dimensional wire-to-wire corona discharge. After having identified the most suitable algorithm, we carry on to two-dimensional wire-to-wire discharges and compare the numerical results with experiment data for different floor densities.