This article presents a model to describe the effects of non-equilibrium plasma discharges on gas temperature and species concentration, in the set of equations governing the combustion phenomena. Based on the results reported in the literature, the model is constructed by analysing the channels through which the electric energy is deposited. The two main channels by which the electrons produced during the discharge impact the flow are considered: (1) the excitation and the subsequent relaxation of electronic states of nitrogen molecules which leads to an ultrafast increase of gas temperature and species dissociation within the discharge characteristic time; and (2) the excitation and relaxation of vibrational states of nitrogen molecules which causes a much slower gas heating. The model is fully coupled with multi-dimensional flow balance equations with detailed transport coefficients and detailed combustion chemical kinetic mechanisms. This high level of NRP discharge modelling allows computing high Reynolds flows by means of Direct Numerical Simulations and, therefore, a better understanding of plasma-assisted ignition phenomena in practical configurations. A sequence of discharge pulses in air and methane–air mixture in quiescent and turbulent flow configurations are studied with this model. The results show the minor impact of the vibrational energy on mixture ignition and how the increase of the turbulence spreads this vibrational energy and intermediate combustion species around the discharge zone, minimizing the cumulative effect of multiple pulses. In contrast, the production of O atoms during the discharge has a strong impact on the ignition delays and ignition energies (number of discharge pulses). The results also underscore the impact of the initial turbulent flow Reynolds number and the spatial distribution of turbulent eddies, relative to the discharge channel, on the number of pulses needed to ignite the mixture.