Towards robust explicit models for streamer discharges

Computer simulations are an important tool to study and understand the behavior of streamer discharges. Such simulations can computationally be quite costly, because a high-resolution mesh is required to accurately model the growth of streamers. In recent years, the use of adaptive mesh refinement (AMR) and parallelized simulations codes have made it possible to study the evolution of multiple streamers in 3D. However, a problem that often arises with explicit time step methods -- which are the most efficient -- is that very small time steps are required for numerical stability. Two challenging cases will be presented: a positive streamer that stops to grow in a low background field, and a positive streamer reaching a dielectric surface. Model adaptations to allow for larger time steps and more robustness will be discussed.