Multiphysics Simulation of Positive Streamer Discharge in Air Using Finite Element Method

ABSTRACT Streamer discharge modeling by means of the Finite Element Method (FEM) presents a formidable challenge in computational physics due to its nonlinear and convection‐dominated characteristics that cause numerical instabilities, including negative densities of charged particles. A possible remedy relies on modifying the numerical scheme using flux correction or stabilization techniques, yet their effects on numerical accuracy are unexplored. This study presents a detailed and rigorous implementation of two different FEM approaches: with and without modifications to the numerical scheme. We investigate how different solution strategies, including fully coupled versus staggered schemes and time discretization techniques affect the solution. All FEM approaches are implemented within the open‐source Firedrake framework. A comprehensive comparison against benchmark data of 2D streamer discharge is performed to evaluate the accuracy of each approach and to quantify the impact of the chosen coupling strategy and time discretization on key streamer parameters such as maximum electric field, streamer length, and the total charge. The results show that both approaches provide an accurate description of the streamer dynamics and the resulting discharge channel with varying levels of numerical efficiency. The choice of coupling strategy, inclusion of source stabilization and the time discretization method further alter streamer front dynamics, stability, and computational cost, demonstrating that these numerical design choices in FEM have a measurable impact on the streamer dynamics.