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

Abstract

Please refer to the journal version when citing this work. 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 twodimensional 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.

Bubble-mediated transfer of dilute gas in turbulence

“…It uses the projection method to compute the velocity and pressure and the geometric volume-of-fluid method for the evolution of the interface between two immiscible fluids (Tryggvason, Scardovelli & Zaleski 2011). The Piecewise Linear Interface Calculation geometric interface and flux reconstruction ensures a sharp representation of the interface (Scardovelli & Zaleski 1999; Marić, Kothe & Bothe 2020) and is combined with an accurate height-function curvature calculation and a well-balanced, continuum surface tension model (Brackbill, Kothe & Zemach 1992; Popinet 2018).…”

A massively parallel accurate conservative level set algorithm for simulating turbulent atomization on adaptive unstructured grids

“…Realistic industrial injector geometries for atomization simulations are very complex, including sharp edges and narrow corners, which hinders the meshing task with cartesian grids: the use of unstructured meshes is thus well suited for this type of simulations [1]. Although the literature remains limited about unstructured atomization computations, previous studies on static meshes can be found, such as [2,3,4,5,6,7,8,9] for Volume Of Fluid (VOF) interface capturing techniques [10], or [11,12,13,14,15] for Level Set methods (LS) [16,17].…”

Volume‐of‐fluid based two‐phase flow methods on structured multiblock and overset grids

“…The research on the geometric VOF methods has been a very active field in recent years, which is mainly focused on the interface reconstruction algorithms (e.g., References 18 and 19), interface propagation and advection schemes, 20,21 and especially implementation on unstructured grids for complex geometries (e.g., References 22‐25). The development of the geometric VOF method has been reviewed in the most recent study, 26 and interested readers are referred to the above papers and references therein.…”