We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uniquely solvable. In addition, they also ensure energy dissipation in many typical scenarios. Through extensive numerical experiments, we demonstrate the schemes' robustness, accuracy and efficiency.

翻译：本文针对一类Wasserstein梯度流提出了两种时间离散格式。这些格式设计用于保持质量守恒与正性，且具有唯一可解性。此外，在多数典型场景下它们还能保证能量耗散特性。通过大量数值实验，我们验证了该格式的鲁棒性、精确性与计算效率。