A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases (Communications in Computational Physics, 2014)
Assumed having axial symmetry, the streamer discharge is often describedby a fluid model in cylindrical coordinate system, which consists of convection dominated (diffusion) equations with source terms, coupled with a Poisson's equation.Without additional care for a stricter CFL condition or special treatment to the negative source term, popular methods used in streamer discharge simulations, e.g., FEM-FCT, FVM, cannot ensure the positivity of the particle densities for the cases in attaching gases. By introducing the positivity-preserving limiter proposed by Zhang andShu [15] and Strang operator splitting, this paper proposes a finite difference schemewith a provable positivity-preserving property in cylindrical coordinate system, forthe numerical simulation of streamer discharges in non-attaching and attaching gases.Numerical examples in non-attaching gas (N2) and attaching gas (SF6) are given toillustrate the effectiveness of the scheme.