  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.
