VOF Introduction
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On the VOF method for sharp interface and bounded phase fraction: derivation, discretization and implementation in OpenFOAM
The volume of fluid (VOF) method was extensively used to capture phase interface multiphase problems \cite{hirt1981volume}. In VOF method, the fluids on either side of the interface are marked by an indicator function, also known as phase fraction, is used to distinguish between two different fluids. In practise, several numerical aspects should be tackled in the solving procedure. The first one is that the exact position of the interface is not known explicitly and special techniques need to be applied to capture a well defined interface as part of the solution algorithm. It is quite common that the first order convection scheme (e.g., upwind scheme) would produces very diffusive results. In certain cases it may be suitable if the variable interface's exact position is not important. However, in the VOF method, a diffusive convection scheme smash the bubble/water interface shape and the predictions cannot be used. Several numerical techniques were developed to handle this problem, such as the simple line interface calculation (SLIC) \cite{noh1976slic} and the piecewise linear interface calculation (PLIC) \cite{youngs1982time}. Methods that employ these ideas give good approximation of the shape of the interface and they allow for proper calculation of the fluxes through faces of the control volumes. However, their application is often restricted to structured grids with simple shapes of the control volumes. Moreover, since estimation of a spatial orientation of the interface from the distribution of the volume fraction needs a substantial number of numerical operations, interface reconstruction methods increase the computational effort. On the other hand, the high resolution interface capturing (HRIC) \cite{muzaferija1998computation} and the compressive interface capturing scheme for arbitrary meshes (CICSAM) \cite{ubbink1999method} can also be used to predict sharp interface. Unlike geometric interface reconstruction methods, the high resolution schemes do not introduce geometrical representation of the interface but try to satisfy the aforementioned conditions by properly chosen discretization scheme.
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