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A comprehensive analysis of streamer discharges is important for understanding the underlying discharge physics in terms of charged particle transport, space charge effects, ionization, attachment, and electric field enhancement, among other parameters. As the initial stage of lightning inside thunderclouds and in high voltage systems, streamer discharges play a significant role as they are the first self-sustained ionized channels that may develop from enhanced electric field regions. Therefore, this thesis aims to conduct a numerical study on streamer discharge dynamics in air under the high voltage and thundercloud conditions.

The streamer models are implemented using the Finite Element Method (FEM) and Finite Difference Method (FDM) in different dimensions, and the findings are compared with the results reported in the literature to understand the numerical aspects of streamer discharge behavior. The humidity effect on streamer discharges is analyzed under high voltage and thundercloud conditions. The local streamer-to-hot-gas discharge transition is studied by applying uniform and prescribed, rapidly increasing background electric fields to represent both the classical streamer discharge development between hydrometeors and the effect of relativistic runaway electron activity within thunderclouds.

The results show that the streamer velocity reduces during the streamer propagation stage as the absolute humidity increases, which is valid for the absolute humidity levels, electrode configurations, applied voltage waveforms, and the numerical methods considered in this thesis. The behavior is attributed to the presence of water molecules in air, which increase the electron attachment, and electron-positive water cluster ion recombination rates, resulting in a low electron density and reduced conductivity in the streamer channel.

In the attempt to understand lightning initiation inside clouds, three different water drop configurations are considered inside a thundercloud. Within the considered simulation time, only a positive streamer is generated from a single water drop, whereas the two and three water drop systems develop both positive and negative streamers. The electrical discharges in a gap are significantly influenced by the presence or absence of simultaneous streamers in other air gaps. The findings obtained from the single drop and two drop configurations indicate that relative humidity levels representative of thundercloud conditions have only a minor influence on both positive and negative streamer dynamics. A collision of both the positive and negative streamers can be observed within two water droplets inside a thundercloud under both imposed electric fields. The maximum gas temperature exceeds 1000 K and a possible mechanism for localized leader inception is identified under a rapidly increasing electric field only.