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

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

Comparison of methods for curvature estimation from volume fractions

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. The numerical studies presented in this work find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost for dynamic interfaces when the interface reconstruction and advection are coupled to a two-phase Navier-Stokes solver

A Collation and Analysis of Two-Dimensional Unsplit Conservative Advection Methods for Volume of Fluid at Interfaces

abstract: The goal of this paper was to do an analysis of two-dimensional unsplit mass and momentum conserving Finite Volume Methods for Advection for Volume of Fluid Fields with interfaces and validating their rates of convergence. Specifically three unsplit transport methods and one split transport method were amalgamated individually with four Piece-wise Linear Reconstruction Schemes (PLIC) i.e. Unsplit Eulerian Advection (UEA) by Owkes and Desjardins (2014), Unsplit Lagrangian Advection (ULA) by Yang et al. (2010), Split Lagrangian Advection (SLA) by Scardovelli and Zaleski (2003) and Unsplit Averaged Eulerian-Lagrangian Advection (UAELA) with two Finite Difference Methods by Parker and Youngs (1992) and two Error Minimization Methods by Pilliod Jr and Puckett (2004). The observed order of accuracy was first order in all cases except when unsplit methods and error minimization methods were used consecutively in each iteration, which resulted in second-order accuracy on the shape error convergence. The Averaged Unsplit Eulerian-Lagrangian Advection (AUELA) did produce first-order accuracy but that was due to a temporal error in the numerical setup. The main unsplit methods, Unsplit Eulerian Advection (UEA) and Unsplit Lagrangian Advection (ULA), preserve mass and momentum and require geometric clipping to solve two-phase fluid flows. The Unsplit Lagrangian Advection (ULA) can allow for small divergence in the velocity field perhaps saving time on the iterative solver of the variable coefficient Poisson System.Dissertation/ThesisMasters Thesis Mechanical Engineering 201

On estimating the interface normal and curvature in PLIC-VOF approach for 3D arbitrary meshes

Volume of fluid (VOF) method with its Piecewise Linear Interface Calculation (PLIC) reconstruction algorithm is one of the most popular approaches in numerical simulation of interfacial flows with a wide range of applications in different areas. In an effort to evaluate the similarity of the PLIC-generated planes in comparison with the exact interface, a point-cloud, based on the polygon centers of PLIC planes is extracted, which later is used to form a triangular grid that represents the estimated interface. The main objective of this article is to evaluate the interface geometrical properties based on the extracted triangular grid of the interface. The methods presented in this article, characterized by a higher spatially convergence ratio, are compared with the commonly used methods. The proposed methods are tested for two 3-dimensional general test cases, where an evident improvement is seen in calculation accuracy and spatial convergence of the errors of interface normal vector and curvature.This work has been financially supported by MCIN/AEI/10.13039/ 501100011033 Spain, project PID2020-115837RBI00. E. Schillaci acknowledges the financial support of the Programa Torres Quevedo (PTQ2018-010060).Peer ReviewedPostprint (author's final draft