A VOLUME OF FLUID METHOD FOR FREE SURFACE FLOWS AROUND SHIP HULLS

This investigation continues the development of an anti-diffusive volume of fluid method [1] by improving accuracy through the addition of an artificial diffusion term, with a negative diffusion coefficient, to the original advection equation describing the evolution of the fluid volume fraction. The advection and diffusion processes are split into a set of two partial differential equations (PDEs). The improved anti-diffusive Volume of Fluid (VOF) method is coupled with a two-fluid flow solver to predict free surface flows and illustrated by examples given in two-dimensional flows. The first numerical example is a solitary wave travelling in a tank. The second example is a plunging wave generated by flow over a submerged obstacle of prescribed shape on a horizontal floor. The computational results are validated against available experimental data.

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Volume of fluid methods for immiscible-fluid and free-surface flows

Chemical Engineering Journal ◽

10.1016/j.cej.2007.12.035 ◽

2008 ◽

Vol 141 (1-3) ◽

pp. 204-221 ◽

Cited By ~ 153

Author(s):

Vinay R. Gopala ◽

Berend G.M. van Wachem

Keyword(s):

Free Surface ◽

Volume Of Fluid ◽

Free Surface Flows ◽

Immiscible Fluid ◽

Surface Flows

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A Simple Verification Test for Nonlinear Flow Calculations Around a Ship Hull Steadily Advancing in Calm Water

Journal of Ship Research ◽

10.5957/jsr.2012.56.3.162 ◽

2012 ◽

Vol 56 (03) ◽

pp. 162-169

Author(s):

Francis Noblesse ◽

Lijue Wang ◽

Chi Yang

Keyword(s):

Free Surface ◽

Boundary Conditions ◽

Free Surface Flows ◽

Wave Profile ◽

Surface Flows ◽

Ship Hulls ◽

Euler Flow ◽

Numerical Predictions ◽

Calm Water ◽

Analytical Relations

Simple analytical relations that can readily be applied to verify a critical aspect of numerical predictions of fully nonlinear free-surface flows around ship hulls steadily advancing in calm water are given. The relations do not involve the flow field equations; that is, they are only based on the boundary conditions at the ship hull surface and at the free surface. These boundary conditions have a predominant influence on free-surface flows around advancing ship hulls. The analytical relations are exact for inviscid flows, and can be applied to numerical methods that solve either the Laplace equation (potential-flow methods) or the Euler flow equations (CFD Euler-flow methods). They provide a simple test to verify if numerical predictions given by nonlinear potential-flow or Euler-flow methods correctly satisfy the hull-surface and free-surface boundary conditions along the contact curve between the hull surface and the free surface. The relations might also be used to verify CFD methods that solve the RANS equations if they are applied at the edge of the viscous boundary layer. The analytical test can identify an inconsistency, which might point to a "method issue" related to a feature of a numerical method (e.g., a numerical-differentiation scheme) or an "implementation issue" in the implementation of the method (e.g., a poor discretization). For purposes of illustration, the test is applied to predictions of flows around the Wigley parabolic hull given by two CFD methods that solve the Euler equations with fully nonlinear boundary conditions at the free surface. This illustrative example demonstrates that the test can indeed be useful to identify numerical inaccuracies. The analytical relations can also be used to determine experimental values of the flow velocity at a ship wave profile that correspond to measurements of the wave profile.

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A Novel Algorithm of Advection Procedure in Volume of Fluid Method to Model Free Surface Flows

ISRN Applied Mathematics ◽

10.5402/2012/521012 ◽

2012 ◽

Vol 2012 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

M. J. Ketabdari ◽

H. Saghi

Keyword(s):

Free Surface ◽

Volume Of Fluid ◽

Free Surface Flows ◽

Navier Stokes ◽

Adjacent Cell ◽

Volume Of Fluid Method ◽

Governing Equations ◽

Model Free ◽

Coarse Grids ◽

Fluid Cell

In this study, the developed procedure of advection in volume of fluid (VOF) method is presented for free surface modeling. The fluid is assumed to be incompressible and viscous and therefore, Navier-Stokes and continuity are considered as governing equations. Applying Youngs’ algorithm in staggered grids, it is assumed that fluid particles in the cell have the same velocity of the cell faces. Therefore, fluxes to neighboring cells are estimated based on cell face velocities. However, these particles can show different velocities between two adjacent cell faces. In developed model, the velocity in mass center of fluid cell is evaluated to calculate fluxes from cell faces. The performance of the model is evaluated using some alternative schemes such as translation, rotation, shear test, and dam break test. These tests showed that the developed procedure improves the results when using coarse grids. Therefore, the Modified Youngs-VOF (MYV) method is suggested as a new VOF algorithm which models the free surface problems more accurately.

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