A volume-of-fluid method for incompressible free surface flows

Abstract

SUMMARYThis paper proposes a hybrid volume-of-fluid (VOF) level-set method for simulating incompressible twophase flows. Motion of the free surface is represented by a VOF algorithm that uses high resolution differencing schemes to algebraically preserve both the sharpness of interface and the boundedness of volume fraction. The VOF method is specifically based on a simple order high resolution scheme lower than that of a comparable method, but still leading to a nearly equivalent order of accuracy. Retaining the mass conservation property, the hybrid algorithm couples the proposed VOF method with a level-set distancing algorithm in an implicit manner when the normal and the curvature of the interface need to be accurate for consideration of surface tension. For practical purposes, it is developed to be efficiently and easily extensible to three-dimensional applications with a minor implementation complexity. The accuracy and convergence properties of the method are verified through a wide range of tests: advection of rigid interfaces of different shapes, a three-dimensional air bubble's rising in viscous liquids, a two-dimensional dam-break, and a three-dimensional dam-break over an obstacle mounted on the bottom of a tank. The standard advection tests show that the volume advection algorithm is comparable in accuracy with geometric interface reconstruction algorithms of higher accuracy than other interface capturing-based methods found in the literature. The numerical results for the remainder of tests show a good agreement with other numerical solutions or available experimental data.

An anti‐diffusive volume of fluid method for interfacial fluid flows

“…Figure 7 presents the time histories of the total height of water at the two locations: (a) x 1 = 2.228 m and (b) x 2 = 2.725 m. The variations between prediction and experimental results may be associated with wave overturning and merging which are very complicated physical phenomena to model as well as compressibility and viscosity. Similar discrepancies between measured data and numerical modelling results are observed in alternative numerical approaches such as VOF, level set and SPH methods (see, for example, Colagrossi and Landrini [23], Abdolmaleki et al [24], Ferrari et al [25], Park et al [26]). Such a comment assumes the experimental data are error free.…”

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

“…The VOF method was typically related to finite difference methods (FDM) [105,167] and finite volume methods (FVM) [96,113,121,165]. Nevertheless, it is also extensively used in the context of finite element method (FEM) [9,41,74,119,134,147,231].…”

Fully-Coupled Balanced-Force VOF Framework for Arbitrary Meshes with Least-Squares Curvature Evaluation from Volume Fractions

“…A hybrid approach was introduced by Williams [10], using the first derivative of a convolution kernel to evaluate the interface normals and a finite-difference method to calculate the curvature from the interface normals. Recent efforts to find more accurate ways to determine the interface curvature have mainly focused on VOF methods with height functions (HF) [6,9,[12][13][14][15] and coupled VOF-LS methods [16][17][18][19][20].…”