Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations

有限体积方案求解非线性聚集-破碎人口平衡方程的收敛性分析

Convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage population balance equations

本文分析了有限体积方案在求解聚集、破碎及耦合过程中的稳定性与收敛性，证明了该方案在不同网格下对纯破碎问题具有二阶收敛性，而在非均匀网格上对非均匀网格仅显示一阶收敛性。

Scharfetter-Gummel格式对聚集-扩散方程的变分收敛及扩散消失极限

Variational convergence of the Scharfetter-Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit

本文利用变分方法研究了聚集-扩散方程的半离散Scharfetter-Gummel格式的收敛性，提出适用于任意非负扩散常数的新梯度结构，同时证明了离散到连续及零扩散极限的收敛性，并恢复了基于2-Wasserstein距离的Otto梯度流结构。

The Scharfetter--Gummel scheme for aggregation-diffusion equations

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, …

一种正向且满足熵的有限体积方案用于Baer-Nunziato模型

A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer-Nunziato Model

本文提出了一种放松方案，用于近似Baer-Nunziato两相流模型的熵耗散弱解，证明了相分数、相密度和相内能在无额外限制条件下的正性，并展示了该方案在计算效率和精度上的优势。

Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach

In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with external potentials, optimal transport problems, and aggregation-diffusion models. Based on the Energetic Variational Approach, a trajectory equation is first derived by using the balance between the maximal dissipation principle and least action principle. By a convex-splitting technique, we propose energy dissipating numerical schemes for the trajectory equati…

一类连续性方程的全离散能量耗散且守恒的离散梯度粒子方法

Fully discrete energy-dissipative and conservative discrete gradient particle methods for a class of continuity equations

针对一类具有变分结构的非线性连续性方程，提出满足正则化能量相容性的粒子方法，结合离散梯度时间积分器实现全离散层面的能量耗散与多物理量守恒，并通过数值算例验证特性。