We propose and study a fully implicit finite volume scheme for the pressureless Euler-Poisson-Boltzmann equations on the one dimensional torus. Especially, we design a consistent and dissipative discretization of the force term which yields an unconditional energy decay. In addition, we establish a discrete analogue of the modulated energy estimate around constant states with a small velocity. Numerical experiments are carried to illustrate our theoretical results and to assess the accuracy of our scheme. A test case of the literature is also illustrated.

翻译：本文提出并研究了一维环面上无压欧拉-泊松-玻尔兹曼方程的全隐式有限体积格式。特别地，我们设计了一种相容且耗散的力项离散格式，该格式能保证能量无条件衰减。此外，我们在具有小速度的常值状态附近建立了调制能量估计的离散类比。通过数值实验验证了理论结果并评估了格式的精度。同时，文中还展示了一个文献中的基准测试算例。