The theory of point vortex dynamics has existed since Kirchhoff's proposal in 1891 and is still under development with connections to many fields in mathematics. As a strong simplification of the concept of vorticity it excels in computational speed for vorticity based fluid simulations at the cost of accuracy. Recent finding by Stefanella Boatto and Jair Koiller allowed the extension of this theory on to closed surfaces. A comprehensive guide to point vortex dynamics on closed surfaces with genus zero and vanishing total vorticity is presented here. Additionally fundamental knowledge of fluid dynamics and surfaces are explained in a way to unify the theory of point vortex dynamics of the plane, the sphere and closed surfaces together with implementation details and supplement material.

翻译：点涡动力学理论自 Kirchhoff 于 1891 年提出以来一直存在，至今仍在发展，并与数学的诸多领域存在联系。作为涡量概念的一种高度简化，它在基于涡量的流体模拟中具有计算速度快的优势，但代价是精度损失。Stefanella Boatto 和 Jair Koiller 近期的发现使得该理论得以扩展到闭曲面上。本文为零亏格且总涡量为零的闭曲面上的点涡动力学提供了一个全面的指南。此外，文章以统一平面、球面及闭曲面上点涡动力学理论的方式阐述了流体动力学和曲面相关的基础知识，并提供了实现细节与补充材料。