Coupled Flow Guidelines

The Simcenter STAR-CCM+ Coupled Flow model and Coupled Implicit Solver make available several parameters which allow control of stability and convergence for practical CFD cases:

The CFL Number property of the Coupled Implicit and Coupled Explicit solvers controls the size of the local time-steps that are used in the time-marching procedure these two solvers employ.
Generally speaking, for a steady-state simulation, a larger CFL number increases the local pseudo-time step size and produces faster convergence. Thus, use the largest CFL number possible while still ensuring that the solver remains within the bounds of stability. (This means that the solver does not start reducing corrections, or hitting temperature and pressure limits, and that the residual has a healthy downward trend.)
The Explicit Relaxation property is a scaling factor that is used to relax all corrections explicitly before they are applied to the variables. It is intended to add stability in cases where the solver’s first-order linearization of a second-order discretization has trouble. The default value is 0.3, which results in 30% of the corrections being applied. Use a value less than 1.0 to limit the applied corrections explicitly.

The Positivity Rate Limit (an expert property of the Coupled Flow Model) defines the amount that temperature, a positive definite quantity, is allowed to decrease when corrections are applied at each iteration. It is expressed as a percentage of the current value.

The default is 0.2, which says temperature is not allowed to decrease by more than 20% (there is no upward limit). If temperature corrections are reduced to meet the Positivity Rate Limit, then all other variable corrections are equally scaled in an attempt to keep everything changing at the same rate.

Note

The last two Coupled Flow properties are linked, in that the Explicit relaxation factor is applied to the corrections first, then the Positivity Rate Limit condition is checked. It is possible that the Explicit relaxation factor could reduce temperature corrections such that the Positivity Rate Limit does not get invoked where it otherwise would.

Deactivate the Preconditioning Enabled option (an expert property of the Coupled Flow Model) when you are trying to capture unsteady phenomena at small time scales (for instance, in an aeroacoustics analysis). Deactivate this property when the Integration property is set to either Implicit or Explicit.

Setup Recommendations

For steady flow, the default value for the CFL Control Method property for the Coupled Implicit solver is Automatic; the CFL number is controlled automatically. In combination with the default explicit relaxation of 0.3, this provides a good combination of speed and robustness for most cases. The Target AMG Cycles property of the Coupled Implicit > Expert Driver node can be increased above the default of 4 to provide potentially faster convergence, or decreased for improved robustness.
For unsteady flow, the default value for the CFL Control Method property for the Coupled Implicit solver is a CFL number of 50.0. With small physical time steps, this number can be greatly increased from 1,000 to 100,000.
The coupled explicit solver uses a default constant CFL of 1.0. Any higher value generally results in numerical instability.
If an approximate initial solution is used (uniform values), smaller CFL number values are required at startup.
You can employ the linear ramp capability of the Coupled Implicit solver, to automate desired change of the CFL number during the simulation.
A low CFL number value of 0.1, or even lower, may be required for startup of some difficult problems (for example, hypersonics or combustion). To ensure that the solver stability is maintained during the entire simulation, use the linear ramp to increase the CFL number based on iteration count.
Depending on the problem (such as very high-speed flow or mesh quality issues) you could use an explicit relaxation factor as low as 0.2 or 0.25. Very difficult cases may require a value of 0.15 to be able to maintain non-linear stability.
Besides the CFL number and the explicit relaxation factor, a practical way to keep hypersonic simulations within physical bounds is to use a lower value for the Positivity Rate Limit. The default value is 0.2, although for extreme hypersonic cases it may be necessary to use values as low as 0.05.

Mesh Quality Considerations

Mesh quality does influence the quality of the numerical results, irrespective of the setup: coupled vs. segregated solver, discretization schemes...
On a mesh of a given quality and sufficient fineness, higher-order schemes yield more accurate results than lower-order ones. For a given cell count, aim to optimize the grid quality because a better mesh gives a more accurate solution regardless of the differencing schemes that are used and other parameters.
With a poor-quality mesh, the gradient limiter is invoked more often, thus affecting its nominal second-order accuracy. Grid skewing is an important contributing factor (much more than grid stretching) to the loss in nominal accuracy of the solution. Grid design (distribution of cell size, local refinement using feature edges, boundary region, or volume shapes) is important in maximizing the accuracy for a given effort. Two grids with the same number of cells may lead to discretization errors that differ by an order of magnitude. Thus, improving mesh quality is a top priority.
When solving steady-state problems on fine meshes, start with a much coarser mesh, and then successively refine the mesh by reducing the base size. For example:
- Design the desired mesh for the highest cell count affordable.
- Increase the base size by a factor of 8 and start the computation with this coarse mesh.
  You may require lower under-relaxation values for the coarsest mesh, but iterations are fast and this does not increase the computing effort much.
- After the convergence criteria are satisfied or maximum specified number of iterations is reached, halve the mesh base size, remesh, and restart the simulation. Repeat until the final mesh size is reached.
In this way, you obtain faster convergence on finer grids by providing a good initial solution. Usually, one needs only a third or a quarter of the number of iterations that would be needed if starting with an initial guess, like constant or zero values.

In addition, you obtain solutions on a series of grids which are systematically refined (same design, only base sizes reduced), which allows for an estimate of discretization errors using Richardson extrapolation. For example, if base size is reduced by a factor of 2 and second-order discretization is used, discretization errors on the finest mesh are equal to one third of the difference between solutions on the finest and next coarser grid. For base size reduction by a factor of 1.5, the errors amount to about 80% of the difference in the two solutions.