Interaction between flames and plasmas are the guiding thread of this work. Nanosecond Repetitively Pulsed (NRP) discharges are non-thermal plasmas which have shown interesting features for combustion control. They can interact with flames not only through heat, but also chemically by producing active species. In this work, fully-coupled plasma assited combustion simulations are targeted. To achieve this goal, plasma discharge capabilities are built in the low temperature plasma code, AVIP. The corresponding numerical methods, as well as validation cases regarding each set of equations, are first presented. To simulate plasma discharges, the coupled drift-diffusion equations and the Poisson equation are considered. AVIP is coupled to the AVBP code which solves the reactive Navier-Stokes equations to describe combustion phenomena. In a second part, we start by constructing and validating a fully-detailed chemistry for methane-air mixtures in zero-dimensional reactors before reducing it for multi dimensional simulations. The multi-dimensional streamer simulation capabilities of the code are then assessed using simple chemistries. All the validated parts of the code come together in a fully detailed simulation of ignition using NRP discharges. We finish by discussing phenomenological models built upon the knowledge that we gained from fully-detailed simulations. In a last part, finally, attempt to solve the Poisson and generalized Poisson equations using neural networks, which have a potential for speedup compared to classical linear solvers, is carried out.