Arabian Journal for Science and Engineering

, Volume 39, Issue 2, pp 669–684 | Cite as

A Modification to SLIC and PLIC Volume of Fluid Models using New Advection Method

Research Article - Civil Engineering


In this paper, modified volume of fluid method based on flux correct transport (FCT) and Youngs’ VOF (YV) method using new advection method are presented. These methods are from simple line interface construction and piecewise linear interface construction methods. The developed model in this study is based on the Navier–Stokes equations (NSE) which describe the laminar flow of an incompressible viscous fluid. To model turbulence, the coupled Navier–Stokes and standard k−ɛ model as the Reynolds average NSE are used. These equations are discretized using finite difference method on the Cartesian staggered grids and solved using simplified marker and cell method. The free surface is displaced using the volume of fluid method based on FCT and Youngs’ algorithms. In these methods, for staggered grids, fluxes to neighboring cells are estimated based on cell face velocities. It means that fluid particles in the cell have the same velocity of the cell faces. However, in practice, these particles have a variable velocity between velocities of two adjacent cell faces. In the modified models of this research, the velocity in mass center of fluid cell is estimated and used to calculate fluxes from cell faces. The performance of the modified scheme has been evaluated using a number of alternative schemes taking into account translation, rotation; shear test and dam break on dry bed. Finally, Airy waves are generated by these models. The results showed that the modified models are more accurate than the original ones.


Flux correct transport Youngs’ VOF method New advection method Navier–Stokes equations Shear test Error estimation 



Flux corrected transport


Finite difference method


Modified flux corrected transport


Modified Youngs’ VOF


Navier–Stokes equations


Numerical wave tank


Reynolds average Navier–Stokes equations


Simple line interface calculation


Simplified marker and cell


Sum square error


Sum absolute error


Piecewise linear interface construction


Three Diagonal Matrix Algorithm


Volume of fluid

List of Symbols


Colour function


Source term including acceleration due to gravity in the i direction


Kinetic energy


Dynamic pressure


Reynolds number




Velocity component in the x direction


Velocity component in the y direction


Dissipation rate


Time step


Mesh size in the x direction


Mesh size in the y direction


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Copyright information

© King Fahd University of Petroleum and Minerals 2013

Authors and Affiliations

  1. 1.Faculty of EngineeringFerdowsi UniversityMashhadIran
  2. 2.Faculty of Marine TechnologyAmirkabir University of TechnologyTehranIran

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