Arabian Journal for Science and Engineering

, Volume 39, Issue 2, pp 669–684

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

Research Article - Civil Engineering

DOI: 10.1007/s13369-013-0688-9

Cite this article as:
Saghi, H. & Ketabdari, M.J. Arab J Sci Eng (2014) 39: 669. doi:10.1007/s13369-013-0688-9
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Abstract

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.

Keywords

Flux correct transportYoungs’ VOF methodNew advection methodNavier–Stokes equationsShear testError estimation

Abbreviations

FCT

Flux corrected transport

FDM

Finite difference method

MFCT

Modified flux corrected transport

MYV

Modified Youngs’ VOF

NSE

Navier–Stokes equations

NWT

Numerical wave tank

RANSE

Reynolds average Navier–Stokes equations

SLIC

Simple line interface calculation

SMAC

Simplified marker and cell

SSE

Sum square error

SAE

Sum absolute error

PLIC

Piecewise linear interface construction

TDMA

Three Diagonal Matrix Algorithm

VOF

Volume of fluid

List of Symbols

F

Colour function

gi

Source term including acceleration due to gravity in the i direction

k

Kinetic energy

p

Dynamic pressure

Re

Reynolds number

t

Time

u

Velocity component in the x direction

v

Velocity component in the y direction

ɛ

Dissipation rate

Δt

Time step

Δx

Mesh size in the x direction

Δy

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