26.5.2 Setting FAS Multigrid Parameters

For most calculations, you will not need to modify any FAS multigrid parameters once you have set the number of coarse grid levels. If, however, you encounter convergence difficulties, you may consider the following suggested procedures.

Recall that FAS multigrid is used only by the density-based explicit formulation.

Combating Convergence Trouble

Some problems may approach convergence steadily at first, but then the residuals will level off and the solution will "get stuck.'' In some cases (e.g., long thin ducts), this convergence trouble may be due to multigrid's slow propagation of pressure information through the domain. In such cases, you should turn off multigrid by setting Multigrid Levels to 0 in the Solution Controls task page.

"Industrial-Strength'' FAS Multigrid

In some cases, you may find that your problem is converging, but at an extremely slow rate. Such problems can often benefit from a more aggressive form of multigrid, which will speed up the propagation of the solution corrections. For such problems, you can try the "industrial-strength'' multigrid settings.

These settings are very aggressive and assume that the solution information passed through the multigrid levels is somewhat accurate. For this reason, you should only attempt the procedure described here after you have performed enough iterations that the solution is off to a good start. Using "industrial-strength'' multigrid too early in the calculation process--when the solution is far from correct--will not help convergence and may cause the calculation to become unstable, as very incorrect values are propagated quickly to the original grid. Note also that while these multigrid settings will usually reduce the total number of iterations required to reach convergence, they will greatly increase the computation time for each multigrid cycle. Thus the solver will be performing fewer but longer iterations.

The strategy employed is as follows:

• Increase the number of iterations performed on each grid level before proceeding to a coarser level

• Increase the number of iterations performed on each grid level after returning from a coarser level

• Allow full correction transfer from one level to the next finer level, instead of transferring reduced values of the corrections

• Do not smooth the interpolated corrections when they are transferred from a coarser grid to a finer grid

You can set all of the parameters for this strategy under FAS Multigrid Controls in the Multigrid tab in the Advanced Solution Controls dialog box (Figure  26.5.2) and then continue the calculation.

Solution Controls Advanced...

Figure 26.5.2: The Advanced Solution Controls Dialog Box

Increasing the number of iterations performed on each grid level before proceeding to a coarser level (the value of $\beta_1$ described in this section in the separate Theory Guide) will improve the solution passed from each finer grid level to the next coarser grid level. Try increasing the value of Pre-Sweeps (under FAS Multigrid Controls, not under Algebraic Multigrid Controls) to 10.

Increasing the number of iterations performed on each level after returning from a coarser level will improve the corrections passed from each coarser grid level to the next finer grid level. Errors introduced on the coarser grid levels can therefore be reduced before they are passed further up the grid hierarchy to the original grid. Try increasing the value of Post-Sweeps (under FAS Multigrid Controls, not under Algebraic Multigrid Controls) to 10.

By default, the full values of the multigrid corrections are not transferred from a coarser grid to a finer grid; only 60% of the value is transferred. This prevents large errors from transferring quickly up to the original grid and causing the calculation to become unstable. It also prevents a "good'' solution from propagating quickly to the original grid. However, by increasing the Correction Reduction to 1, you can transfer the full values from coarser to finer grid levels, speeding the propagation of the solution and, usually, the convergence as well. The Species Correction Reduction sets the factor by which to reduce the magnitude of the species corrections to stabilize the multigrid calculation. This item appears only when species transport is being modeled.

When the corrections on a coarse grid are passed back to the next finer grid level, the values are, by default, interpolated and then smoothed. Disabling the smoothing so that the actual value in a coarse grid cell is assigned to the fine grid cells that comprise it can also aid convergence. To disable smoothing, set the Correction Smoothing to 0. Large discontinuities between cells will be smoothed out implicitly as a result of the additional Post-Sweeps performed.

The Courant Number Reduction sets the factor by which to reduce the Courant number for coarse grid levels (i.e., every level except the finest). Some reduction of time step (such as the default 0.9) is typically required because the stability limit cannot be determined as precisely on the irregularly shaped coarser grid cells.