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How do I setup my mesh to best capture VOF Waves?by Priyanka Cholleti

on 9/23/2015

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  •    •    • Categories: Meshing Strategies, Volume of Fluid (VOF) Products: STAR-CCM+ Version Applicable: N/A Article Number:

4927

The VOF wave models are used to set boundary conditions to simulate surface gravity waves on a light fluid-heavy fluid interface.

They are for three-dimensional cases only, and are used with the Volume of Fluid (VOF) multiphase model in STAR-CCM+.

They are typically used along with the 6-DOF Motion model for marine applications. When created, VOF Waves provide field

functions that can be used to initialize the VOF calculation and to provide suitable profiles at boundaries. The VOF Waves model,

when selected, also activates a region condition and a boundary condition to control damping of the waves near boundaries in order

to reduce wave reflections. The wave profile and the wave phase velocity depend on water depth, wave height and current.

There are several types of waves which can be simulated:  

 

: A first order wave is modeled with a first order approximation to the Stokes theory of waves. This approximationFirst Order Wave

generates waves that have a regular periodic sinusoidal profile.

 

: A fifth order wave is modeled with a fifth order approximation to the Stokes theory of waves. This wave moreFifth Order Wave

closely resembles a real wave than one generated by the first order method.

This wave theory is only valid for Ursell numbers less than 30. The Ursell number indicates the nonlinearity of long surface gravity

waves on a fluid layer. It is derived from the Stokes wave expansion, a perturbation series for nonlinear periodic waves, in the

long-wave limit of shallow water — when the wavelength is much larger than the water depth. Then the Ursell number   is definedU

as:

: the wave height,   the difference between the elevations of the wave crest and trough,H that is,

: the mean water depthh

: the wavelength, which has to be large compared to the depth,   ≫  .λ λ h

So the Ursell parameter   is the relative wave height   /   times the relative wavelength   /   squared.U H h λ h

For long waves (  λ ≫  ) with small Ursell number,   h U ≪ 32 π  / 3 ≈ 100, linear wave theory is applicable.2

 

The main goal when simulating waves is to resolve the wave shape. Create a good mesh which is refined in the correct regions

along with using an appropriate time-step size. Simulating waves is essentially solving time and space- so cell size and time-step

size go hand in hand. You are recommended to have a CFL < 1.0, with a target value is 0.5.

 

Mesh settings to follow:

 

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λ – Wavelength is the distance between crest to crest

H – Height of wave

Cell length (horizontal) = λ/n where n is the number of cells

n = 40–100, 80 is the recommended value

Cell length (vertical) = H/m where m is the number of cells

m = 20–40, 40 is the recommended value

CFL of free surface below 0.5

Time integration set to 2  ordernd

Time-step Size = Wave period ÷ (2.4 × n)

Boundary conditions to incorporate for plane progressive waves:

 

For a generic case, the top and inlet boundary surfaces would be set up to be velocity inlets. The bottom and outlet boundary

surface would be set up as pressure outlets. The sides of the tank or domain can be specified as either slip walls or symmetry

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planes. At the outlet, you are advised that The Flat Wave model be incorporated (on the calm waterline), this Flat Wave model adds

damping to attenuate the vertical momentum in the field to reduce the reflected wave. Aim for a fixed damping length of around ~2

.wavelengths

Some caveats with modeling waves in STAR-CCM+:

Time-step size and mesh cell size must agree. Both mesh size and time-step go hand in hand.

These guidelines are for a 3D model, a quasi 2D model serves for faster run times.

Since waves do not rely on viscosity, setting the Viscous Regime to Inviscid also yields faster run times.

 See also:

Why doesn't the free surface in my VOF marine simulation appear as expected?

What does the Enable Theory Comparison option for VOF Waves mean?

STAR-CCM+ Documentation sections:

Tutorial Guide > Motion > Body Force Propeller Method: Marine Self-Propulsion

User Guide > Modeling Physics > Modeling Multiphase Flow > Working with VOF Waves