A spectral element method for modelling streamer discharges in low-temperature atmospheric-pressure plasmas
A spectral element method for modelling streamer discharges in low-temperature atmospheric-pressure plasmas
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DOI：
10.1016/j.jcp.2022.111378
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发表时间：
2021-11
期刊：
影响因子：
--
通讯作者：
I. Semenov;K. Weltmann
中科院分区：
文献类型：
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作者：
I. Semenov;K. Weltmann
流光是发生在大气压和亚大气压下的气体中的电离前沿。流光的数值研究是重要的实际应用，但具有挑战性，由于这种放电类型的多尺度性质。本文介绍一种模拟流注放电的谱元方法。该方法是笛卡尔网格，但可以扩展到非结构网格上使用。流光模型是基于泊松方程的电势和电子连续性方程。泊松方程离散通过谱方法的基础上的积分表示的解决方案。分层庞加莱-斯特克洛夫（HPS）格式用于求解所得方程组。采用间断Galerkin谱元法求解电子连续性方程。的DGSEM扩展的扩散通量的另一种定义。如果需要的话，使用子单元有限体积法来稳定DGSEM方案。整个模拟方案是通过解决一些测试问题和再现以前的研究结果进行验证。自适应网格细化用于减少未知数的数量。所提出的方法被发现是足够快的，用于在实际应用中。该方法的灵活性提供了一个有趣的机会，扩大范围的问题，可以解决在低温等离子体放电的数值研究。
Streamers are ionization fronts that occur in gases at atmospheric and sub-atmospheric pressures. Numerical studies of streamers are important for practical applications but are challenging due to the multiscale nature of this discharge type. This paper introduces a spectral element method for modelling streamer discharges. The method is developed for Cartesian grids but can be extended to be used on unstructured meshes. The streamer model is based on the Poisson equation for the electric potential and the electron continuity equation. The Poisson equation is discretized via a spectral method based on the integral representation of the solution. The hierarchical Poincaré - Steklov (HPS) scheme is used to solve the resulting set of equations. The electron continuity equation is solved by means of the discontinuous Galerkin spectral element method (DGSEM). The DGSEM is extended by an alternative definition of the diffusion flux. A subcell finite volume method is used to stabilize the DGSEM scheme, if required. The entire simulation scheme is validated by solving a number of test problems and reproducing the results of previous studies. Adaptive mesh refinement is used to reduce the number of unknowns. The proposed method is found to be sufficiently fast for being used in practical applications. The flexibility of the method provides an interesting opportunity to broaden the range of problems that can be addressed in numerical studies of low-temperature plasma discharges.