Numerical Error Analysis and Improvement Methods for Streamer Discharge Simulation

In the field of discharge research for electrical equipment, the microscopic mechanisms of streamer discharge are difficult to obtain through experiments. Numerical simulations, however, provide an effective approach to solving this issue. Traditional numerical methods in streamer discharge simulations often face problems such as large discretization errors, numerical oscillations, and high computational resource demands, which affect the accuracy and efficiency of the simulation results. To address these issues, this study introduces an efficient numerical method that combines the reduced-order element finite element method with an adaptive mesh strategy. By utilizing the open-source numerical computation library FEniCSx, this approach enables point-wise estimation and control of numerical errors in streamer discharge simulations, offering a more efficient and accurate numerical solution strategy for discharge simulations of complex electrical equipment. In the future, the proposed method could be further extended to more complex time-varying processes and three-dimensional problems, exploring a broader range of application scenarios.