Volume Fraction Reinitialization

The Volume Fraction Reinitialization model allows for a dynamic modification of the free surface by sharpening or smearing the interface. This can improve the modeling and reduce computational cost.

In some VOF simulations, interface smearing can occur due to large local CFL numbers caused by excessively large time steps, small cells, or as a result of poorly converged solutions. Sometimes, excessive smearing can be the result of general remeshing or when changing the mesh resolution. To address these issues, the Volume Fraction Reinitialization model can be used to accelerate the recovery of sharp interfaces.

The Volume fraction reinitialization methodology in Simcenter STAR-CCM+ is based on an approach described in [601] which aims at maintaining a smooth profile and transition width of a phase field function during the convective transport. The relevant step is characterized as solving a non-linear convection-diffusion equation to steady state. Given an initial (potentially smeared) volume fraction field $α_{o}$ and the interface normal vector $\vec{n_{0}} = \frac{\nabla α_{0}}{| | \nabla α_{0} | |}$ , the following equation is solved to steady-state in pseudo-time $τ$ :

Figure 1. EQUATION_DISPLAY

\partial_{t} α + \nabla \cdot (α (1 - α) \vec{n_{0}}) = \nabla \cdot (ϵ \nabla α)

(2620)

The second term on the left-hand side of Eqn. (2620) represents compression of the volume fraction field along the prescribed interface normal $\vec{n_{0}}$ (kept constant throughout the procedure). The term on the right-hand side of Eqn. (2620) represents an isotropic diffusion proportional to a user-defined parameter $ϵ$ .

In steady-state, these contributions balance and the solution exhibits a boundary layer of a width that is proportional to

ϵ

, in which the transition of the volume fraction from 0 to 1 takes place. For the method to be convergent with respect to mesh-size,

ϵ

should be proportional to (a power of) the mesh-size h, given as:

Figure 2. EQUATION_DISPLAY

{ϵ = ϵ}_{x} = \frac{w (x) h}{2}

(2621)

where $w (x)$ is the target interface width function for the volume fraction field. For $w (x) = 0$ both compressive and diffusive fluxes are disabled, therefore deactivating the reinitialization process (locally).

The solution to Eqn. (2620) preserves the volume of the given phase up to the solver tolerance.

If the phase density is constant, phase volume conservation implies mass conservation. Mixture density and enthalpy are updated to account for redistribution of volume fractions. For variable density, the conservative redistribution of volume is not sufficient for mass conservation. Therefore, the approach does not conserve momentum and energy, which introduces small consistency errors. As a result, every reinitialization step introduces a minor conservation error, proportional to the scale of the reinitialized interface.