Development of volume of fluid methods to model free surface flow using new advection algorithm

Technical Paper

DOI: 10.1007/s40430-013-0045-7

Cite this article as:
Ketabdari, M.J. & Saghi, H. J Braz. Soc. Mech. Sci. Eng. (2013) 35: 479. doi:10.1007/s40430-013-0045-7


In this paper, a new advection algorithm is presented to model free surface flows using volume of fluid method. To model the fluid flow, Navier–Stokes equations are solved as governing equations using two-step projection method on the Cartesian staggered grids. In the volume of fluid method, several algorithms such as flux-corrected transport (FCT) and Youngs’ algorithms are used to model the free surface. 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, the particles velocity varies between two adjacent cell faces velocities. In the present research, modified Youngs’ and flux-corrected transport methods are presented. In these methods, the velocity in mass center of fluid cell is estimated and used to calculate cell face fluxes. The performance of the modified schemes has been evaluated using a number of alternative schemes taking into account translation, rotation, shear test and dam break on dry bed. The results showed that the modified Youngs’ method is more accurate than the original one particularly in coarse grid. It is also more accurate than the modified flux-corrected transport method.


Navier–Stokes equationFree surface flowsVolume of fluid (VOF)Shear testAdvection

List of symbols


Time (s)


Velocity vector (m2/s)


Hydrodynamic pressure (N/m2)


Kinematic fluid viscosity (m2/s)


Gravity acceleration (m/s2)


Scalar function of VOF method

\( U^{n} \)

Velocity field in old time level (m/s)

\( \hat{U} \)

Intermediate velocity field (m/s)

\( U^{n + 1} \)

New velocity field (m/s)

\( {\text{conv}}^{n} \)

Convection term

\( {\text{Diff}}^{n} \)

Diffusion term

\( B^{n} \)

Body force including gravity acceleration


Mesh sizes in the x direction


Mesh sizes in the y direction

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2013

Authors and Affiliations

  1. 1.Faculty of Marine TechnologyAmirkabir University of TechnologyTehranIran
  2. 2.Department of Civil EngineeringFerdowsi University of MashhadMashhadIran