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

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

gVOF: An open-source package for unsplit geometric volume of fluid methods on arbitrary grids

The gVOF package implements several accurate and efficient geometric volume of fluid (VOF) methods on arbitrary grids, either structured or unstructured with convex or non-convex cells, based on multidimensional unsplit advection and piecewise linear interface calculation (PLIC) schemes, with the purpose of facilitating and extending the use of advanced unsplit geometric VOF methods in new or existing computational fluid dynamics codes. The package includes a complete and self-contained set of routines for VOF initialization, interface reconstruction and fluid advection, and uses as external libraries a set of publicly available in-house tools to perform several analytical and geometrical operations. These operations may involve handling of high-complex non-convex flux polyhedra, even with self-intersecting faces, which are robustly and efficiently treated in this work without the need of costly techniques based on convex decomposition. Results for the accuracy, computational efficiency, and volume (local and global) conservation properties of different combinations of the implemented advection and reconstruction methods are presented for several numerical tests on structured and unstructured grids. An extensive comparison with results obtained by other authors using advanced geometric VOF methods shows the outstanding performance of the gVOF package in terms of efficiency and accuracy. To demonstrate the performance of the package in solving complex two-phase flow problems, the implemented methods are combined with an existing in-house code to simulate the impact of a water drop on a free surface.The authors gratefully acknowledge the joint support of the Spanish Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación and FEDER through projects DPI2017-87826-C2-1-P and DPI2017-87826-C2-2-P, and the Spanish Ministerio de Ciencia e Innovación - Agencia Estatal de Investigación (MCIN/ AEI / 10.13039/501100011033) through projects PID2020-120100GB-C21 and PID2020-120100GB-C22

An iterative interface reconstruction method for PLIC in general convex grids as part of a Coupled Level Set Volume of Fluid solver

Reconstructing the interface within a cell, based on volume fraction and normal direction, is a key part of multiphase flow solvers which make use of piecewise linear interface calculation (PLIC) such as the Coupled Level Set Volume of Fluid (CLSVOF) method. In this paper, we present an iterative method for interface reconstruction (IR) in general convex cells based on tetrahedral decomposition. By splitting the cell into tetrahedra prior to IR the volume of the truncated polyhedron can be calculated much more rapidly than using existing clipping and capping methods. In addition the root finding algorithm is designed to take advantage of the nature of the relationship between volume fraction and interface position by using a combination of Newton's and Muller's methods. In stand-alone tests of the IR algorithm on single cells with up to 20 vertices the proposed method was found to be 2 times faster than an implementation of an existing analytical method, while being easy to implement. It was also found to be 3.4–11.8 times faster than existing iterative methods using clipping and capping and combined with Brent's root finding method. Tests were then carried out of the IR method as part of a CLSVOF solver. For a sphere deformed by a prescribed velocity field the proposed method was found to be up to 33% faster than existing iterative methods. For simulations including the solution of the velocity field the maximum speed up was found to be approximately 52% for a case where 12% of cells lie on the interface. Analysis of the full simulation CPU time budget also indicates that while the proposed method has produced a considerable speed-up, further gains due to increasing the efficiency of the IR method are likely to be small as the IR step now represents only a small proportion of the run time

A new isosurface extraction method on arbitrary grids

The development of interface-capturing methods (such as level-set, phase-field or volume of fluid (VOF) methods) for arbitrary 3D grids has further highlighted the need for more accurate and efficient interface reconstruction procedures. In this work, we propose a new method for the extraction of isosurfaces on arbitrary polyhedra that can be used with advantage for this purpose. The isosurface is extracted from volume fractions by a general polygon tracing procedure, which is valid for convex or non-convex geometries, even with non-planar faces. The proposed method, which can be considered as an extension of the marching cubes technique, produces consistent results even for ambiguous situations in polyhedra of arbitrary shape. To show the reproducibility of the results presented in this work, we provide the open source library isoap, which has been developed to implement the proposed method and includes test programs to demonstrate the successful extraction of isosurfaces on several grids with polyhedral cells of different types. We present results obtained not only for isosurface extraction from discrete volume fractions resulting from a volume of fluid method, but also from data sets obtained from implicit mathematical functions and signed distances to scanned surfaces. The improvement provided by the proposed method for the extraction of isosurfaces in arbitrary grids will also be very useful in other fields, such as CFD visualization or medical imaging.The authors gratefully acknowledge the support of the Spanish Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación and FEDER through projects DPI2017-87826-C2-1-P and DPI2017-87826-C2-2-P

An unstructured Finite-Volume Level Set / Front Tracking method for capillary flows

In this thesis the unstructured Finite-Volume hybrid Level Set / Front Tracking method (LENT) for immiscible two-phase flows is extended to enable the simulation of capillary flows. The major contributions are a more accurate interface curvature approximation, an accuracy driven pressure velocity coupling algorithm, an approximation technique for consistent mass fluxes for momentum convection and two novel approaches for the computation of volume fractions from triangulated surfaces. All proposed techniques and algorithms are devised for unstructured Finite-Volume meshes. The improved curvature approximation uses a signed distance field as input and utilizes surface-mesh/volume-mesh mappings to reduce curvature variation in interface normal direction. A novel, local correction approach is introduced to further reduce the curvature error in cells intersected by the interface. To ensure a prescribed solution accuracy, an iterative, accuracy driven pressure velocity coupling algorithm is presented that builds on the established segregated solution algorithms. The necessity of consistent mass fluxes for momentum convection in the presence of differing fluid densities is analyzed. For interface advection methods that do not utilize phase-specific volumetric fluxes, a method to obtain approximate, consistent mass fluxes is proposed. The resulting improvements for capillary flows are demonstrated using canonical verification and validation test cases. Two novel algorithms to compute volume fractions on unstructured volume meshes from oriented triangle surfaces meshes are introduced, one based on geometric intersections and one based on approximation and adaptive refinement. Intended for the phase indicator calculation in the context of Level Set / Front Tracking methods, both algorithms are shown to be sufficiently accurate to initialize volume fractions also for the Volume-of-Fluid method. In fact, test cases demonstrate that both approaches’ accuracy is only limited by the resolution of the surface mesh

A Higher-Order VOF Interface Reconstruction Scheme for Non-Orthogonal Structured Grids - with Application to Surface Tension Modelling

The volume-of-fluid (VOF) method [24] is widely used to track the interface for the purpose of simulating liquid-gas interfacial flows numerically. The key strength of VOF is its mass conserving property. However, interface reconstruction is required when geometric properties such as curvature need to be accurately computed. For surface tension modelling in particular, computing the interface curvature accurately is crucial to avoiding so-called spurious or parasitic currents. Of the existing VOF-based schemes, the height-function (HF) method [10, 16, 18, 42, 46, 53] allows accurate interface representation on Cartesian grids. No work has hitherto been done to extend the HF philosophy to non-orthogonal structured grids. To this end, this work proposes a higher-order accurate VOF interface reconstruction method for non-orthogonal structured grids. Higher-order in the context of this work denotes up to 4 th-order. The scheme generalises the interface reconstruction component of the HF method. Columns of control volumes that straddle the interface are identified, and piecewise-linear interface constructions (PLIC) are computed in a volume-conservative manner in each column. To ensure efficiency, this procedure is executed by a novel sweep-plane algorithm based on the convex decomposition of the control volumes in each column. The PLIC representation of the interface is then smoothed by iteratively refining the PLIC facet normals. Rapid convergence of the latter is achieved via a novel spring-based acceleration procedure. The interface is then reconstructed by fitting higher-order polynomial curves/surfaces to local stencils of PLIC facets in a least squares manner [29]. Volume conservation is optimised for at the central column. The accuracy of the interface reconstruction procedure is evaluated via grid convergence studies in terms of volume conservation and curvature errors. The scheme is shown to achieve arbitrary-order accuracy on Cartesian grids and up to fourth-order accuracy on non-orthogonal structured grids. The curvature computation scheme is finally applied in a balanced-force continuum-surface-force (CSF) [4] surface tension scheme for variable-density flows on nonorthogonal structured grids in 2D. Up to fourth-order accuracy is demonstrated for the Laplace pressure jump in the simulation of a 2D stationary bubble with a high liquid-gas density ratio. A significant reduction in parasitic currents is demonstrated. Lastly, second-order accuracy is achieved when computing the frequency of a 2D inviscid oscillating droplet in zero gravity. The above tools were implemented and evaluated using the Elemental®multi-physics code and using a vertex-centred finite volume framework. For the purpose of VOF advection the algebraic CICSAM scheme (available in Elemental®) was employed