Compressive VOF Module

Stream supports incompressible gas-liquid and multi-liquid interface capturing through the compressive_vof module. The module solves transport equations for liquid volume fractions (VOF), builds mixture density and viscosity from phase properties, and adds optional surface-tension and contact-angle forcing to the momentum equation.

Enable the module by adding loadModule: compressive_vof to the run control file:

loadModule: compressive_vof
{
  ... standard run control file content
}

Control File Setup

The module expects phase property definitions and VOF state definitions in the run control file.

Phase Properties

Two run-control variables define phase properties:

liquidPhases: one or more named incompressible liquid phases.
gasPhase: incompressible gas phase used for the non-liquid remainder.

Each phase must provide rho and mu.

Example phase setup

liquidPhases: <
  water=incompressible(rho=998.2 kg/m/m/m, mu=1.0e-3 kg/m/s),
  oil=incompressible(rho=850.0 kg/m/m/m, mu=4.0e-3 kg/m/s)
>
gasPhase: <
  air=incompressible(rho=1.225 kg/m/m/m, mu=1.8e-5 kg/m/s)
>

The liquid fraction for each phase is tracked separately. The gas fraction is computed as:

\[\alpha_{gas} = 1 - \sum_i \alpha_{liquid,i}\]

Initial Conditions

The module requires VOF initialization in initialCondition (uniform) or initialConditionRegions (regional states), using a vof=[phase=value,...] list whose phase names match those in liquidPhases.

Uniform VOF initial condition

initialCondition: <p=0 Pa, v=0.0 m/s, vof=[water=1.0, oil=0.0]>

Regional VOF initialization

initialConditionRegions: <
  default=state(vof=[water=0.0, oil=0.0]),
  slug=state(vof=[water=1.0, oil=0.0]),
  regions=[
    inBox(p1=[0.0, 0.0, 0.0], p2=[0.02, 0.002, 0.002], composition=slug)
  ]
>

Boundary Conditions

For incompressibleInlet, subsonicInlet, totalPressureInlet, inflow, and farfield boundaries, a vof list is required.

subsonicInlet accepts velocity or flow-rate specifications and requires T through the common inlet interface. With flowCompressibility: incompressible and constant phase properties, this temperature does not enable heat transport or change the phase densities. For example:

Inlet=subsonicInlet(mdot=0.144 lbm/s,T=68 F,vof=[water=1.0,oil=0.0])

incompressibleInlet can specify the same flow without T.

Inlet VOF specification

boundary_conditions: <
  Inlet=incompressibleInlet(v=[0.2 m/s, 0.0 m/s, 0.0 m/s], vof=[water=1.0, oil=0.0]),
  Outlet=fixedPressureOutlet(p=0.0 Pa),
  Wall=noslip
>

Periodic boundaries obtain VOF from the paired cells; no vof list is needed. Use the standard translational or rotational periodic setup.

For no-slip walls, an optional per-boundary static contact angle override can be provided:

Wall=noslip(contactAngle=35 deg)

If contactAngle is provided, units must be degrees and the value must be in [0,180].

VOF Transport and Property Options

The following variables control VOF transport and property blending.

VOF and Mixture Property Controls
Variable	Allowed Values	Default	Description
`vofInviscidFlux`	`FOU`, `IG`, `MIG`, `FBIC`, `TVD`	`FOU`	Inviscid flux for liquid-volume-fraction transport.
`vofViscosity`	real	`0.0`	Extra numerical diffusion coefficient used in VOF assembly.
`vofViscosityBlend`	`linear`, `harmonic`	`linear`	Mixture laminar viscosity blending model.
`overUnderFillingCorrection`	`on`, `off`	`off`	Enables face-level over/under-fill correction in non-FOU VOF advection.

vofViscosityBlend=linear uses arithmetic blending by volume fraction. vofViscosityBlend=harmonic uses harmonic blending and is often preferable for high viscosity-ratio flows.

The solver also performs a final boundedness projection on each VOF solve collapse: individual liquid fractions are clipped to [0,1] and renormalized if their sum exceeds 1.

VOF Equation Solver Options

vofEquationOptions configures the VOF linear solve controls.

`vofEquationOptions` Entries
Entry	Allowed Values	Default	Description
`linearSolver`	`SGS`, `FSGS`, `LSGS`	`SGS`	Linear solver used for `vofStar`.
`relaxationFactor`	real in `(0,1]`	`0.5`	Relaxation factor for VOF equation update.
`maxIterations`	integer `>= 0`	`5`	Maximum VOF linear iterations per nonlinear iteration.

Example:

vofEquationOptions: <linearSolver=SGS, relaxationFactor=0.6, maxIterations=8>

Nonlinear Convergence

Add vof to either convergence-tolerance list to include the liquid equations in the nonlinear stopping criterion:

convergenceAbsoluteTolerance: <default=1e-8, vof=1e-8>
convergenceRelativeTolerance: <vof=1e-4>

Every liquid must satisfy its absolute or relative tolerance, along with the other active equations. Absolute tolerances use the RV: residuals in kg/s; relative tolerances use each liquid’s first positive residual in the current time step. References reset at each step, including restart entry. There is no separate gas-fraction equation.

Tolerances must be finite, nonnegative numbers. Once enabled, vof overrides default in each list; a missing entry uses 1e-30. An active legacy convergenceTolerance overrides the absolute tolerance and sets the relative tolerance to 1e-30. Omit it when using the lists above.

Without an explicit vof entry, VOF residuals do not affect stopping. Reaching maxIterationsPerTimeStep still advances the solution and prints a warning for any liquid that has not met its requested tolerance.

Surface Tension, Curvature, and Contact Angle

Surface tension is activated by defining sigma.

Surface-Tension and Interface-Geometry Controls
Variable	Allowed Values	Default	Description
`sigma`	real (N/m)	not set	Surface tension coefficient.
`vof_curvature_type`	`computed`, `none`	`computed`	Curvature source: geometric computation or constant value.
`kappaAnalytical`	real	`0.0`	Constant curvature used when `vof_curvature_type=none`.
`vof_curvature_regularization_type`	`none`, `clamp`	`none`	Optional post-processing regularization of computed curvature.
`vof_curvature_abs_max`	real `>0` (when clamp active)	`1.0e6`	Absolute curvature limit for `clamp` regularization.
`vof_curvature_regularization_band`	real in `[0,0.5)`	`0.0`	Apply clamp only for interface cells with `band < capillaryColor < 1-band`.
`vof_contact_angle_model`	`none`, `static`, `dynamic`	`none`	Wall contact-angle model for no-slip boundaries.
`vof_contact_angle_deg`	real in `[0,180]` deg	`90.0`	Baseline angle; for static model, this is the imposed value.
`vof_dynamic_contact_angle_coeff`	real `>=0`	`9.0`	Dynamic angle coefficient in Cox-Voinov-lite relation.
`vof_dynamic_contact_angle_min_deg`	real in `[0,180]` deg	`5.0`	Lower bound for dynamic contact angle.
`vof_dynamic_contact_angle_max_deg`	real in `[0,180]` deg	`175.0`	Upper bound for dynamic contact angle.

The dynamic contact-angle model uses:

\[\theta^3 = \theta_0^3 + C \cdot Ca\]

where \(\theta_0\) is from vof_contact_angle_deg, \(C\) is vof_dynamic_contact_angle_coeff, and \(Ca\) is a local wall-relative capillary number. The computed angle is then clamped by the min/max dynamic bounds.

If a no-slip boundary supplies contactAngle=..., that boundary value overrides the global vof_contact_angle_deg for that boundary patch. This override is active only when vof_contact_angle_model is static or dynamic.

Output and Diagnostics

When plot output is written, the module writes per-phase VOF scalar fields:

output/vof_<liquidName>_sca.<cycle>_<modelName>
output/vof_<gasName>_sca.<cycle>_<modelName>

Add vofResidual to plot_output to write residuals for all liquid phases (disabled by default):

plot_output: vofResidual

Each liquid produces output/vofResidual_<liquidName>_sca.<cycle>_<modelName>. There is no gas residual field because no separate gas-fraction equation is solved.

Values are signed, unnormalized liquid mass-equation residuals (kg/s), interpolated to nodes. Plot the absolute value for magnitude; interpolation can smooth or cancel neighboring residuals. The RV: log instead sums absolute cell residuals.

These fields follow the standard end-of-step residual timing and plot_output_iteration setting described in Field Data Written to Output Directory.

Module scalar diagnostics:

output/liquidVolume.dat: total liquid volume for each liquid phase vs. cycle/time.
output/capillaryDiagnostics.dat with columns:
- ncycle
- stime
- maxAbsKappa
- maxCapillaryCFL
- totalLiquidVolumeDriftAbs
- totalLiquidVolumeDriftRel

The capillary CFL diagnostic is estimated as:

\[CFL_{\sigma} = \Delta t \sqrt{\frac{|\sigma|}{\rho V}}\]

evaluated near interface cells.

Complete Example

Minimal compressive_vof setup for an air-water case

loadModule: compressive_vof
{
  liquidPhases: <water=incompressible(rho=998.2 kg/m/m/m, mu=1.0e-3 kg/m/s)>
  gasPhase: <air=incompressible(rho=1.225 kg/m/m/m, mu=1.8e-5 kg/m/s)>

  initialCondition: <p=0 Pa, v=0.0 m/s, vof=[water=0.0]>

  boundary_conditions: <
    Inlet=incompressibleInlet(v=[0.1 m/s, 0.0 m/s, 0.0 m/s], vof=[water=1.0]),
    TubeWall=noslip(contactAngle=35 deg),
    Outlet=fixedPressureOutlet(p=0.0 Pa)
  >

  vofEquationOptions: <linearSolver=SGS, relaxationFactor=0.6, maxIterations=8>
  vofInviscidFlux: MIG
  vofViscosityBlend: harmonic
  overUnderFillingCorrection: on

  sigma: 0.072 N/m
  vof_curvature_type: computed
  vof_curvature_regularization_type: clamp
  vof_curvature_abs_max: 2.0e4
  vof_contact_angle_model: dynamic
  vof_contact_angle_deg: 90.0
  vof_dynamic_contact_angle_coeff: 9.0
  vof_dynamic_contact_angle_min_deg: 20.0
  vof_dynamic_contact_angle_max_deg: 160.0
}

Notes

The current surface-tension model uses a single sigma value for all interfaces.
Multiple liquid phases are supported in transport and property blending.
For gasPhase, if multiple gas entries are provided, the last one read is used for rhoGas and muGas.