Numerical Methods and Comparisons for 1D and Quasi 2D Fluid Streamer Propagation Models

In this work, we propose and compare four different strategies to simulate the fluid model for streamer propagation in one-dimension (1D) and quasi two-dimension (2D), which consists of a Poisson's equation for particle velocity and two continuity equations for particle transport. Each strategy involves of one method for solving Poisson's equation and the other for solving continuity equations, and a total variation diminishing three-stage Runge-Kutta method in temporal discretization. The numerical methods for Poisson's equation include finite volume method, discontinuous Galerkin methods, mixed finite element method and least-squared finite element method. The numerical method for continuity equations is chosen from the family of discontinuous Galerkin methods. The accuracy tests and comparisons show that all of these four strategies are suitable and competitive in streamer simulations from the aspects of accuracy and efficiency. Results show these methods are compatible. By applying any strategy in real simulations, we can study the dynamics of streamer propagations in both 1D and quasi 2D models.