We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling, respectively. 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：我们讨论对可憎和有吸引力的Euler-Poisson等式进行结构保留的数字分解,这些等式分别在流体成形和自重模型中找到应用。该计划是完全分离的,结构保持,因为它保持离散能源法,以及超单体异域特性,如密度的假设性和特定恒温的最低限度原则。我们详细讨论了算法细节以及索赔属性的证据。我们提出计算实验,以证实我们的分析结论,并演示该方法的计算能力。