Numerical Simulations for the Quasi-3D Fluid Streamer Propagation Model: Methods and Applications (Communications in Computational Physics, 2020)
In this work, we propose and compare four different strategies for simulatingthe fluid model of quasi-three-dimensional streamer propagation, consisting ofPoisson's equation for the particle velocity and two continuity equations for particletransport in the cylindrical coordinate system with angular symmetry. Each strategyinvolves one method for solving Poisson's equation, a discontinuous Galerkinmethod for solving the continuity equations, and a total variation-diminishing RungeKuttamethod in temporal discretization. The numerical methods for Poisson's equationinclude discontinuous Galerkin methods, the mixed finite element method, andthe least-squares finite element method. The numerical method for continuity equationsis the Oden-Babuška-Baumann discontinuous Galerkin method. A slope limiterfor the DG methods in the cylindrical coordinate system is proposed to conserve thephysical property. Tests and comparisons show that all four strategies are compatiblein the sense that solutions to particle densities converge. Finally, different types ofstreamer propagation phenomena were simulated using the proposed method, includingdouble-headed streamer in nitrogen and SF6 between parallel plates, a streamerdischarge in a point-to-plane gap.
Keywords: Streamer discharge; mixed finite element method; least-squares finite element method; discontinuous Galerkin method; fluid model.