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We present an open-source plasma fluid code for 2D, cylindrical and 3Dsimulations of streamer discharges, based on the Afivo framework that featuresadaptive mesh refinement, geometric multigrid methods for Poisson's equation,and OpenMP parallelism. We describe the numerical implementation of a fluidmodel of the drift-diffusion-reaction type, combined with the local fieldapproximation. Then we demonstrate its functionality with 3D simulations oflong positive streamers in nitrogen in undervolted gaps, using three examples.The first example shows how a stochastic background density affects streamerpropagation and branching. The second one focuses on the interaction of astreamer with preionized regions, and the third one investigates theinteraction between two streamers. The simulations run on up to $10^8$ gridcells within less than a day. Without mesh refinement, they would require$4\cdot 10^{12}$ grid cells.

Simulating streamer discharges in 3D with the parallel adaptive Afivo framework