Unstructured un-split geometrical Volume-of-Fluid methods -- A review

TL;DR

This review paper critically examines unstructured mesh geometrical Volume-of-Fluid methods in 3D, highlighting their challenges, recent research focus areas, and comparing various methods in terms of accuracy and efficiency.

Contribution

It provides a comprehensive, historical, and comparative overview of classical and modern 3D unstructured mesh geometrical VoF methods, emphasizing their complexities and research trends.

Findings

Unstructured meshes pose significant challenges in 3D geometrical VoF methods.

Research is actively addressing interface positioning, normal vector estimation, and computational efficiency.

Methods vary in accuracy and efficiency, with ongoing improvements in handling complex geometries.

Abstract

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.