Free Surface CFL Reference

Limits the time-step size to allow for a sharp interface. This time-step provider is appropriate for free surface flows when the VOF interface crosses meshes that have different CFL numbers, such as from coarse mesh to fine mesh, or has a changing velocity field.

The Free Surface CFL time-step provider sets the time-step based on CFL number weighted by the rate of change of Volume Fraction. This time-step provider is available when the Volume of Fluid (VOF) model or the Mixture Multiphase (MMP) model is activated in the physics continuum.

Smoothing

The Free Surface CFL time-step provider carries out volume-weighted smoothing. The following operation is performed the number of times that is specified in Smoothing Steps.

For a time-step condition variable $Φ$ defined for each control volume $i$ :

Figure 1. EQUATION_DISPLAY

Φ_{i} = \frac{Φ_{i} V_{i} + \sum_{j = 1}^{N} Φ_{j} V_{j}}{V_{i} + \sum_{j = 1}^{N} V_{j}}, \forall i

(94)

where $N$ is the number of neighboring control volumes with volume $V$ .

After smoothing, $Φ$ is used to determine the time-step change factor as:

Figure 2. EQUATION_DISPLAY

f_{Δ t} = \frac{Φ_{\max, \lim i t}}{\max (Φ)}

(95)

where $Φ_{m a x, l i m i t}$ is the specified Max Condition Limit and $\max (Φ)$ is the maximum value of $Φ$ over the whole domain. Note that $Φ$ is always positive.

Table 1. Free Surface CFL Reference
Provided By	Right-click Continua > Physics 1 > Models > Adaptive Time-Step > Time-Step Providers and select New > Free Surface CFL
Example Node Path	Continua > Physics 1 > Models > Adaptive Time-Step > Time-Step Providers > Free Surface CFL
Requires	Time: Implicit Unsteady or PISO Unsteady Material: Multiphase. Multiphase Models: Volume of Fluid (VOF) or Mixture Multiphase (MMP).
Properties	Enable/Disable, Max Condition Limit, Smoothing Steps,Cut-off Percentage. See Free Surface CFL Properties.
Activates	Field Functions	Time Step Condition VOF, Free Surface CFL Proposal See Field Functions.

Free Surface CFL Properties

Enable/Disable

See Adaptive Time-Step Provider Common Properties.

Max Condition Limit

The maximum value of the time-step condition. This value is $Φ_{m a x, l i m i t}$ that is used in Eqn. (95).

Smoothing Steps

The number of smoothing steps. This value specifies the number of times that the volume-weighted smoothing operation (Eqn. (94)) is performed.

Cut-off Percentage

Specifies a percentage $p$ of small/bad cells to be ignored by the Adaptive Time-Step model. The prescribed cut-off percentage is used to find the quantile $t_{q} (p)$ , such that for a given $p$ :

Figure 3. EQUATION_DISPLAY

\frac{# [c e l l s : Δ t_{c} \leq t_{q} (p)]}{# [a l l c e l l s]} \approx p %

(96)

The time-step is then set as $t_{q} (p)$ and any local time-steps that the provider proposes below this value are ignored by the model. The range for this property is 0 (default) to 100.

Field Functions

The following field functions are available when the Free Surface CFL time-step provider is activated.

Time Step Condition VOF: This value is $Φ = C o {\bar{ϕ}}_{t}$ where $C o$ is the Convective Courant (CFL) Number and ${\bar{ϕ}}_{t}$ is the normalized local rate of change of volume fraction.

Free Surface CFL Proposal: The local Free Surface CFL time-step proposal for each individual cell.