In this paper, we study an asymptotic preserving (AP), energy stable and positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann (EPB) system in the quasineutral limit. The key to energy stability is the addition of appropriate stabilisation terms into the convective fluxes of mass and momenta, and the source term. The space-time fully-discrete scheme admits the positivity of the mass density, and is consistent with the weak formulation of the EPB system upon mesh refinement. In the quasineutral limit, the numerical scheme yields a consistent, semi-implicit discretisation of the isothermal compressible Euler system, thus leading to the AP property. Several benchmark numerical case studies are performed to confirm the robustness and efficacy of the proposed scheme in the dispersive as well as the quasineutral regimes. The numerical results also corroborates scheme's ability to very well resolve plasma sheaths and the related dynamics, which indicates its potential to applications involving low-temperature plasma problems.

翻译：本文研究拟中性极限下Euler-Poisson-Boltzmann（EPB）系统的渐近保持、能量稳定且保正性的半隐式有限体积格式。能量稳定的关键在于向质量与动量的对流通量项及源项中添加适当的稳定化项。该时空全离散格式保证质量密度的正性，并在网格细化时与EPB系统的弱形式相容。在拟中性极限下，该数值格式导出等温可压缩Euler系统的一致半隐式离散形式，从而具备渐近保持特性。通过多个基准数值算例验证了所提格式在色散区域与拟中性区域中的鲁棒性与有效性。数值结果同时证实该格式能精确解析等离子体鞘层及其相关动力学行为，表明其在涉及低温等离子体问题中的应用潜力。