Summary

Background

Theory

      

      

Define the change in volume over the timestep Δt by subtract the volumes as follows:

      

Redefine the net volumetric continuity source into a single variable called Q. This refers to the overall rate at which mass is being exchanged between the different phases within a computational cell. It is the net result of the contributions from various phase interaction models incorporated in the simulation. To calculate the value of Q, you would need to consider the individual contributions from the different phase interaction models relevant to your simulation. These models are typically based on physical phenomena and governing equations specific to the system being studied. It's important to note that the specific form of the equation may vary depending on the numerical method and the governing equations used in the simulation. The equation provided here is a general representation of the time-step constraint equation commonly used in multiphase flow simulations.

      

To avoid excessive pressure fluctuations during the simulation the volume change must be limited to a fraction of the cell volume V_c.

      

where:

Δt is the time-step size

C is a dimensionless factor (often referred to as the Courant number or scaling factor) that depends on the numerical scheme and stability criteria of the simulation. In this application it is a scaling factor with an allowable range of 0.001 to 10, the default is 1 (phase mass transfer fills the cell volume per time-step). Modify this value to limit the size of the time-step such that the phase mass transfer in a given cell is never larger than a fraction of the cell volume.

V_c is the volume of the computational cell

Q is the net volumetric continuity source from all participating phase interaction models.

In this equation, the term V_c / Q represents the characteristic time required to transfer the fluid volume within the cell based on the net transfer rate.

Implementation

Follow these step-by-step instructions to setup Volumetric Source adaptive time-step:

1. Open or create a new Simcenter STAR-CCM+ simulation file with VOF or MMP multiphase models selected. Note, the selected physics models depend on the specific problem you are simulating.
   
2. Enable Adaptive Time-Step Model.
   
3. Right click Time-Step Providers located under Continua > Physics > Model Adaptive Time-Step in the Simulation tree. Select Volumetric Source.
   
   
   
4. The Scaling Factor has an allowable range of 0.001 to 10, the default is 1 (phase mass transfer fills the cell volume per time-step). This example uses a value of 0.5, where phase mass transfer fills half (0.5) of the cell volume per time-step.
   
5. Set the maximum allowable timestep under Solvers > Implicit Unsteady, Time-step in the simulation tree. It is important to clip the maximum allowable time-step when there is no phase change present, else the timestep will be too large. This example uses a value of 1E-5 s.
   
6. Set the minimum allowable time-step under Solvers > Adaptive Time-Ste, Minimum Time-Step in the simulation tree. This example uses a value of 1E-8 s. Setting the minimum time-step is important to limit the computation resources required. This can be set a sufficiently small value to limit the computation resources required to solve the calculation.
   
   
7. You may elect to activate the expert options. Verbosity sends additional time-step progress to the Output window. Time-Step Change Factor Bounds are useful when you have large variations in successive step size proposals, you can specify a lower and upper bound for the change factor (ratio) of successive time-steps. A proposed time-step size is then restricted to the specified range.