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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.

MSC:
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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