In this paper, we propose a finite-volume scheme for aggregation-diffusion equations based on a Scharfetter--Gummel approximation of the quadratic, nonlocal flux term. This scheme is analyzed concerning well-posedness and convergence towards solutions to the continuous problem. Also, it is proven that the numerical scheme has several structure-preserving features. More specifically, it is shown that the discrete solutions satisfy a free-energy dissipation relation analogous to the continuous model. Consequently, the numerical solutions converge in the large time limit to stationary solutions, for which we provide a thermodynamic characterization. Numerical experiments complement the study.

翻译：在本文中,我们根据非本地通量术语的Scharfetter-Gummel近似值,提出一个总合-扩散方程式的有限量计划。这个计划是根据对持续问题解决办法的妥善准备和趋同性来分析的。此外,这个数字计划有几种结构保留特征。更具体地说,已经表明离散解决方案满足了类似于连续模型的免费能源消散关系。因此,数字解决方案在大量时限内与固定解决方案相汇合,对此我们提供了热力学特征。数字实验是对研究的补充。