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

  • Research Article - Civil Engineering
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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.

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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

F :

Colour function

g i :

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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Authors and Affiliations

  1. Faculty of Engineering, Ferdowsi University, Mashhad, Iran

    H. Saghi

  2. Faculty of Marine Technology, Amirkabir University of Technology, 424 Hafez Avenue, 15875-4413, Tehran, Iran

    M. J. Ketabdari

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  1. H. Saghi
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  2. M. J. Ketabdari
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Correspondence to M. J. Ketabdari.

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Saghi, H., Ketabdari, M.J. A Modification to SLIC and PLIC Volume of Fluid Models using New Advection Method. Arab J Sci Eng 39, 669–684 (2014). https://doi.org/10.1007/s13369-013-0688-9

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  • DOI: https://doi.org/10.1007/s13369-013-0688-9

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