An asymptotic preserving and energy stable scheme for the Euler-Poisson system under the quasineutral scaling is designed and analysed. Correction terms are introduced in the convective fluxes and the electrostatic potential, which lead to the dissipation of mechanical energy and the entropy stability. The resolution of the semi-implicit in time finite volume in space fully-discrete scheme involves two steps: the solution of an elliptic problem for the potential and an explicit evaluation for the density and velocity. The proposed scheme possesses several physically relevant attributes, such as the the entropy stability and the consistency with the weak formulation of the continuous Euler-Poisson system. The AP property of the scheme, i.e. the boundedness of the mesh parameters with respect to the Debye length and its consistency with the quasineutral limit system, is shown. The results of numerical case studies are presented to substantiate the robustness and efficiency of the proposed method.

翻译：本文设计并分析了一种适用于准中性标度下Euler-Poisson系统的渐近保持与能量稳定格式。通过对对流通量和静电势引入修正项，实现了机械能的耗散和熵稳定性。所提出的半隐式时间离散-空间有限体积全离散格式包含两个步骤：求解电势的椭圆型问题以及显式计算密度和速度。该格式具有多个物理相关属性，例如熵稳定性以及与连续Euler-Poisson系统弱形式的一致性。证明了格式的AP性质，即网格参数相对于德拜长度的有界性及其与准中性极限系统的一致性。数值算例结果证实了所提方法的鲁棒性和有效性。