模拟非附着和附着气体中流注放电的保正格式
A positivity-preserving scheme for the simulation of streamer discharges in non-attaching and attaching gases
摘要:
假设具有轴对称性,流光放电通常由柱坐标系中的流体模型描述,该流体模型由具有源项的对流主导(扩散)方程和泊松方程耦合组成。如果不额外考虑更严格的CFL条件或对负源项的特殊处理,则流光放电模拟中使用的流行方法,例如,FEM-FCT、FVM不能保证吸附气体情况下粒子密度为正。通过引入Zhang和Shu \cite{ppl}提出的保正性限制器和Strang算子分裂,在柱坐标系中提出了一种可证明保正性的有限差分格式,用于非附着和附着气体中流注放电的数值模拟.数值算例表明了格式的有效性,并给出了非附着气体(N $_2$)和附着气体(SF $_6$)的计算结果.
英文摘要:
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 Zhang and Shu \cite{ppl} and Strang operator splitting, this paper proposed 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 (N$_2$) and attaching gas (SF$_6$) are given to illustrate the effectiveness of the scheme.
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