In this work, we propose and compare four different strategies for simulating the fluid model of quasi-three-dimensional streamer propagation, consisting of Poisson's equation for the particle velocity and two continuity equations for particle transport in the cylindrical coordinate system with angular symmetry. Each strategy involves one method for solving Poisson's equation, a discontinuous Galerkin method for solving the continuity equations, and a total variation-diminishing RungeKutta method in temporal discretization. The numerical methods for Poisson's equation include discontinuous Galerkin methods, the mixed finite element method, and the least-squares finite element method. The numerical method for continuity equations is the Oden-Babuška-Baumann discontinuous Galerkin method. A slope limiter for the DG methods in the cylindrical coordinate system is proposed to conserve the physical property. Tests and comparisons show that all four strategies are compatible in the sense that solutions to particle densities converge. Finally, different types of streamer propagation phenomena were simulated using the proposed method, including double-headed streamer in nitrogen and SF₆ between parallel plates, a streamer discharge in a point-to-plane gap.