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A positivity-preserving scheme for the simulation of streamer discharges in non-attaching and attaching gases. (English) Zbl 1373.76206
Summary: Assumed having axial symmetry, the streamer discharge is often described by 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 X. Zhang and C.-W. Shu [J. Comput. Phys. 231, No. 5, 2245–2258 (2012; Zbl 1426.76493)] and Strang operator splitting, this paper proposes a finite difference scheme with a provable positivity-preserving property in cylindrical coordinate system, for the numerical simulation of streamer discharges in non-attaching and attaching gases. Numerical examples in non-attaching gas (N2) and attaching gas (SF6) are given to illustrate the effectiveness of the scheme.

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76W99 Magnetohydrodynamics and electrohydrodynamics
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