Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are traditionally used for handling geometrically complex solution domains that are prevalent when simulating problems of industrial relevance. However, three-dimensional geometrical operations are significantly more complex than their two-dimensional counterparts, which is confirmed by the ratio of publications with three-dimensional results on unstructured meshes to publications with two-dimensional results or support for structured meshes. Additionally, unstructured meshes present challenges in serial and parallel computational efficiency, accuracy, implementation complexity, and robustness. Ongoing research is still very active, focusing on different issues: interface positioning in general polyhedra, estimation of interface normal vectors, advection accuracy, and parallel and serial computational efficiency.

This survey tries to give a complete and critical overview of classical, as well as contemporary geometrical VOF methods with concise explanations of the underlying ideas and sub-algorithms, focusing primarily on unstructured meshes and three dimensional calculations. Reviewed methods are listed in historical order and compared in terms of accuracy and computational efficiency.

几何流体体积（VoF）方法主要支持结构化网格，科学文献中只有少量贡献报告了非结构化网格和三个空间尺寸的结果。传统上，非结构化网格用于处理几何复杂的求解域，在模拟与工业相关的问题时很普遍。但是，三维几何运算比其二维几何运算要复杂得多，这可以通过非结构化网格上具有三维结果的出版物与具有二维结果或支持结构化网格的出版物的比率来证实。另外，非结构化网格在串行和并行计算效率，准确性，实现复杂性和鲁棒性方面提出了挑战。

这项调查试图对经典以及当代的几何VOF方法进行完整而批判的概述，并对有关基本思想和子算法的简要说明，主要集中在非结构化网格和三维计算上。审查的方法按历史顺序列出，并在准确性和计算效率方面进行比较。