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25.11 Setting Algebraic Multigrid Parameters

As mentioned earlier, in most cases the multigrid solver will not require any special attention from you. If, however, you have convergence difficulties or you want to minimize the overall solution time by using more aggressive settings, you can monitor the multigrid solver and modify the parameters to improve its performance. (The instructions below assume that you have already begun calculations, since there is no need to monitor the solver if you do not fit into one of the two categories above.)

To determine whether your convergence difficulties can be alleviated by modifying the multigrid settings, you will check if the requested residual reduction is obtained on each grid level. To minimize solution time, you will check to see if switching to a more powerful cycle will result in overall reduction of work by the solver.

By default, the flexible cycle is used for all equations except pressure correction, which uses a V cycle. Typically, for a flexible cycle only a few (5-10) relaxations will be performed at the finest level and no coarse levels will be visited. In some cases one or two coarse levels may be visited. If the maximum number of fine level relaxations is not sufficient, you may want to increase the maximum number (as described in Section  25.11.1) or switch to a V cycle (as described in Section  25.11).

In the pressure-based segregated algorithm, the pressure correction uses a V cycle by default. If the maximum number of cycles (30 by default) is not sufficient, you can switch to a W cycle (using the Multigrid Controls panel, as described in Section  25.11). Note that for the parallel solver, efficiency may deteriorate with a W cycle. If you are using the parallel solver, you can try increasing the maximum number of cycles by increasing the value of Max Cycles in the Multigrid Controls panel under Fixed Cycle Parameters.

In the pressure-based coupled algorithm and the density-based implicit formulation, there is no pressure correction. Instead, there is a flow correction, which by default uses the F cycle. The density-based explicit formulation uses the V cycle as the default flow correction.

Solve $\rightarrow$ Controls $\rightarrow$ Multigrid...

Specifying the Multigrid Cycle Type

By default, the V cycle is used for the pressure equation in the pressure-based segregated algorithm and the flexible cycle is used for all other equations. In the pressure-based coupled algorithm and the density-based implicit formulation, the F cycle is default for the flow correction. The V cycle is default for the flow correction in the density-based explicit formulation. (See Section  25.6.2 for a description of these cycles.) To change the cycle type for an equation, you will use the top portion of the Multigrid Controls panel (Figure  25.11.1).

For each equation, you can choose Flexible, V-Cycle, W-Cycle, or F-Cycle in the adjacent drop-down list.

Setting the Termination and Residual Reduction Parameters

When you use the flexible cycle for an equation, you can control the multigrid performance by modifying the Termination and/or Restriction criteria for that equation at the top of the Multigrid Controls panel (Figure  25.11.1).

Solve $\rightarrow$ Controls $\rightarrow$ Multigrid...

The Restriction criterion is the residual reduction tolerance, $\beta$ in Equation  25.6-14. This parameter dictates when a coarser grid level must be visited (due to insufficient improvement in the solution on the current level). With a larger value of $\beta$, coarse levels will be visited less often (and vice versa). The Termination criterion, $\alpha$ in Equation  25.6-15, governs when the solver should return to a finer grid level (i.e., when the residuals have improved sufficiently on the current level).

For the V, W, or F cycle, the Termination criterion determines whether or not another cycle should be performed on the finest (original) level. If the current residual on the finest level does not satisfy Equation  25.6-15, and the maximum number of cycles has not been performed, FLUENT will perform another multigrid cycle. (The Restriction parameter is not used by the V, W, and F cycles.)

Setting the AMG Method and the Stabilization Parameters

You can use the Multigrid Controls panel (Figure  25.11.1) to choose between two AMG solvers: aggregative or selective. The aggregative AMG (AAMG) is the default solver that was used in previous versions of FLUENT. The selective AMG (SAMG) solver is available only for scalar equations, and is not available in parallel FLUENT. These two solvers differ in the way the grids are coarsened and in their interpolation method.

The AAMG solver [ 394] builds coarse levels by grouping fine level cells to make coarse level cells, and uses piecewise constant interpolation. The SAMG solver [ 358] builds coarse levels by selecting some of the fine level cells for solution on the coarse level, and tries to approximate the use of linear interpolation.

Due to its use of more accurate interpolation, SAMG has a better convergence rate than AAMG but has a more expensive setup phase. For this reason, AAMG is usually faster if you are only converging one order of magnitude, while SAMG is faster if using a tight multigrid convergence tolerance. SAMG is a good choice for multiphase granular flow problems where a tight convergence tolerance on the pressure equation can be used to avoid volume imbalance errors in the volume fraction equations.

SAMG has advantages in solving problems with strongly varying (anisotropic) diffusive coefficients, which occurs in problems with porous media, conduction with anisotropic thermal conductivities, and multiphase problems. In some cases, using SAMG allows up to a 20% reduction in the number of external iterations for unsteady water-air turbulent flow in bubble columns, and allows increasing the VOF under-relaxation factor in phase separators from 0.2 (when used with AAMG) to 1.

The Multigrid Controls panel (Figure  25.11.1) also allows you to choose a stabilization method. If desired, you can choose the bi-conjugate gradient stabilized method [ 20] ( BCGSTAB) option in order to improve the convergence of the linear solver. BCGSTAB can be preconditioned by any of the AMG solvers and provides stabilization for them.

FLUENT usually builds diagonally dominant matrices for the linear solver. However, this is not always possible. A linear system with highly dominant off-diagonal coefficients may occur during discretization of complex physical models such as multiphase cavitation. Using the BCGSTAB option in such cases can be helpful. In addition, the AMG convergence in parallel can be improved using the BCGSTAB option with AMG.

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