We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling. The scheme is fully discrete and structure preserving in the sense that it maintains a discrete energy law, as well as hyperbolic invariant domain properties, such as positivity of the density and a minimum principle of the specific entropy. A detailed discussion of algorithmic details is given, as well as proofs of the claimed properties. We present computational experiments corroborating our analytical findings and demonstrating the computational capabilities of the scheme.

翻译：本文探讨了在排斥与吸引型Euler-Poisson方程中保持结构特性的数值离散化方法，此类方程广泛应用于流体等离子体与自引力建模。该格式在完全离散化框架下实现结构保持性，具体表现为：满足离散能量守恒律，同时保持双曲型不变域特性（包括密度正定性及比熵极小值原理）。我们详细阐述了算法实现细节，并给出所提特性的理论证明。文中通过数值实验验证了理论分析结论，同时展示了该格式的计算能力。