Multi-Stepping Guidelines

To help you determine whether your simulation would benefit from using multi-stepping, consider whether it has the following characteristics. These characteristics are typical of cases that are well-suited for multi-stepping:

• The time scale of VOF transport (or more specifically the CFL number constraint of the HRIC scheme) is clearly the limiting factor for the global time step size.

  All of the other relevant physical processes should allow time step sizes that are at least twice as long as that required by the volume fraction transport.

• The coupling between the velocity and volume fraction fields is low.

  The main purpose of multi-stepping is to use larger global time steps. As the coupling between the volume fraction and the momentum transport gets weaker, larger time steps become possible. Multi-stepping typically produces a sharper interface than the single-step method. If the coupling between the volume fraction and momentum transport is strong, the multi-stepping resolves the physics better and, consequently, can be less stable than the single-step method for the same time-step size.

  In cases where the volume fraction transport is strongly coupled with other transport process and this coupling dictates the time-step size, multi-stepping is unlikely to improve the computational efficiency.

Explicit Multi-Stepping Guidelines

The explicit multi-stepping approach imposes stability restrictions associated with the explicit discretization. As a result, the following assumptions are made with explicit multi-stepping:

• All time scales are resolved.

  Interface smearing is not possible with explicit multi-stepping, so the sub-step time-step size needs to be small enough to resolve the motion of the free surface everywhere, using the specified maximum number of sub-steps.

• Interface smearing is not an option.

  The single-step method smears the interface if the time steps are too large. Simcenter STAR-CCM+ may require a large number of sub-steps to resolve the interface without smearing. If the maximum number of sub-steps is not sufficient, the interface can be distorted and the simulation may have mass conservation problems.

• Mesh quality is good.

  Distorted cells can cause locally high spurious velocity peaks. When you use single-stepping, the free surface is smeared where the velocity hot-spots appear. This smearing of the interface relaxes numeric calculations and damps the spurious velocities. However, explicit multi-stepping produces a sharp interface that can interact with a poorly-resolved velocity field and exaggerate any numerical issues that are associated with the bad cells.

Implicit Multi-Stepping Guidelines

The implicit multi-stepping solver performs a fixed number of implicit sub-steps for the solution of the volume fraction transport equation. For implicit multi-stepping, the volume fraction transport does not limit the global time-step size, and is not subject to the stability restrictions of the explicit multi-step solver. This methodology inherits its characteristics from the single-step solver, including the ability to allow interface smearing.

As implicit multi-stepping is not bound to time-step size restrictions, many VOF simulation can benefit in the following way:

• If the flow features are resolved sufficiently well at a time-step size that is, for example N times greater than the global time-step, increase the global time-step (by a factor of N) and add the same amount (N) of implicit sub-steps. This approach maintains a sufficient time-step associated with the volume fraction transport to satisfy the CFL constraints without limiting the full flow (global) time-step. Because the global time-steps are much more computationally expensive than sub-steps, this approach can lead to a significant simulation speed-up.
• Similarly, if you encounter that the single-step solver tends to smear the interface at a given time-step size, instead of reducing the global time-step, use the implicit multi-step solver to reduce memory requirements and computational efforts.