Finding Implicit and Explicit Solutions for Initial Value Problems

24.2.2 Choosing a Volume Fraction Formulation

To specify the volume fraction formulation to be used for the VOF and Eulerian multiphase models, select the appropriate Scheme under Volume Fraction Parameters in the Multiphase Model dialog box.

The schemes that are available in ANSYS FLUENT are Explicit and Implicit.

Explicit schemes take on different forms:

Time-dependent with the explicit interpolation scheme: Since the donor-acceptor scheme is available only for quadrilateral and hexahedral meshes, it cannot be used for a hybrid mesh containing twisted hexahedral cells. For such cases, you should use the time-dependent explicit scheme. This formulation can also be used for other cases in which the geometric reconstruction scheme does not give satisfactory results, or the flow calculation becomes unstable. Note that the CICSAM scheme or the modified HRIC scheme can be computationally inexpensive when compared to the geometric reconstruction scheme and improves the robustness and stability of the calculations. The Volume Fraction discretizations, Modified HRIC and CICSAM, are available in the Solution Controls task page when the explicit scheme is selected.

Note that ANSYS FLUENT will automatically enable the transient formulation with first-order discretization for time in the Solution Methods task page.

Time-dependent with the geometric reconstruction interpolation scheme: This formulation should be used whenever you are interested in the time-accurate transient behavior of the VOF solution.
To use this formulation, make sure Explicit is selected as the VOF Scheme in the Solution Methods task page, then select Geo-Reconstruct as the Volume Fraction Discretization scheme in the Solution Methods task page.
Time-dependent with the donor-acceptor interpolation scheme: This formulation should be used instead of the time-dependent formulation with the geometric reconstruction scheme if your mesh contains highly twisted hexahedral cells. For such cases, the donor-acceptor scheme may provide more accurate results.
The Donor-Acceptor spatial discretization scheme is used when Explicit is selected as the Scheme in the Multiphase Models dialog box. Initially, Donor-Acceptor is not available in the Solution Methods task page GUI. To make it available, use the following text command:

solve $\rightarrow$ set $\rightarrow$ expert

You will be asked a series of questions, one of which is
```
Allow selection of all applicable discretization schemes? [no]                  
```
If your response is yes, then many more discretization schemes will be available for your selection. You can now use this formulation by selecting Donor-Acceptor as the Volume Fraction Spatial Discretization in the Solution Methods task page.
The CICSAM scheme gives interface sharpness of the same level as the geometric reconstruction scheme and is particularly suitable for flows with high viscosity ratios between the phases.
To use this formulation, select Explicit as the volume fraction Scheme in the Multiphase Model dialog box, then select CICSAM as the Volume Fraction Spatial Discretization in the Solution Methods task page.

While the explicit time-dependent formulation is less computationally expensive than the geometric reconstruction scheme, the interface between phases will not be as sharp as that predicted with the geometric reconstruction scheme. To reduce this diffusivity, it is recommended that you use the second-order discretization scheme for the volume fraction equations. In addition, you may want to consider turning the geometric reconstruction scheme back on after calculating a solution with the implicit scheme, in order to obtain a sharper interface.

For the geometric reconstruction and donor-acceptor schemes, if you are using a conformal mesh (i.e., if the mesh node locations are identical at the boundaries where two subdomains meet), you must ensure that there are no two-sided (zero-thickness) walls within the domain. If there are, you will need to slit them, as described in Section 6.8.6.

In general, Geo-Reconstruct, Modified HRIC, and CICSAM are applied to cases with sharp interfaces, while First Order Upwind and QUICK are applied to diffused interfaces. Note that Geo-Reconstruct and CICSAM schemes are available with the Eulerian multiphase model, only when the Immiscible Fluid Model is enabled. First Order Upwind is available only for the Eulerian multiphase explicit scheme. It is not available when the Immisible Fluid Model is enabled. However, it can be made available in the GUI for the VOF multiphase explicit scheme when the solve/set/expert text command is invoked

When the Eulerian model is used with the Explicit scheme and the Immiscible Fluid Model is disabled, you can apply First Order Upwind, QUICK, and Modified HRIC. If the Immiscible Fluid Model is enabled, you can apply Geo-Reconstruct, CICSAM, QUICK, and Modified HRIC.

The issues discussed above for the explicit time-dependent formulation also apply to the implicit steady-state and time-dependent formulations, described below. You should take the precautions described above to improve the sharpness of the interface.

Impilict schemes take on the following forms:

Time-dependent with the implicit interpolation scheme: This formulation can be used if you are looking for a steady-state solution and you are not interested in the intermediate transient flow behavior, but the final steady-state solution is dependent on the initial flow conditions and/or you do not have a distinct inflow boundary for each phase.
To use this formulation, select Implicit as the volume fraction Scheme in the Multiphase Model dialog box, and enable a Transient calculation in the General task page.
Steady-state with the implicit interpolation scheme: This formulation can be used if you are looking for a steady-state solution, you are not interested in the intermediate transient flow behavior, and the final steady-state solution is not affected by the initial flow conditions and there is a distinct inflow boundary for each phase. Note that the implicit modified HRIC scheme can be used as a robust alternative to the explicit geometric reconstruction scheme.
To specify the formulation when using the VOF multiphase model, select Implicit as the volume fraction Scheme in the Multiphase Model dialog box, then select First Order Upwind, Second Order Upwind, Modified HRIC, or QUICK as the Volume Fraction Spatial Discretization in the Solution Methods task page. When using the Eulerian multiphase model, select First Order Upwind, QUICK, or Modified HRIC as the Volume Fraction Spatial Discretization in the Solution Methods task page.

Examples

To help you determine the best formulation to use for your problem, some examples that use different formulations are listed below:

jet breakup
Use the explicit scheme (time-dependent with the geometric reconstruction scheme or the donor-acceptor if problems occur with the geometric reconstruction scheme).
shape of the liquid interface in a centrifuge
Use the time-dependent solver with the implicit interpolation scheme.
flow around a ship's hull
Use the steady-state solver with the implicit interpolation scheme.