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

TL;DR

This paper compares four numerical strategies for simulating 1D and quasi-2D fluid streamer propagation models, evaluating their accuracy and efficiency in solving coupled Poisson and continuity equations.

Contribution

It introduces and systematically compares four different numerical strategies combining various methods for Poisson and continuity equations in streamer simulations.

Findings

All four strategies are accurate and efficient.

Methods are compatible and suitable for streamer propagation modeling.

Any strategy can be used for studying streamer dynamics in 1D and quasi-2D.

Abstract

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.