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DQ - ΔQ limiter

 DQ [LIMITER] [OFF | {ON | NXAIR | POINTWISE} \                     [DRMAX drmax] [DTMAX dtmax] [DPMAX dplim] \                     [RELAX dqrlx] [PRINT {ON | OFF}]]

The DQ LIMITER keyword may be used to limit the change in the solution over a single iteration. This may be helpful, especially in the initial stages of a calculation, in maintaining stability, and allow the use of larger CFL numbers than might otherwise be possible.

If the DQ LIMITER keyword is not used, the following default will be applied:

• If all zones are structured, the ΔQ limiter is off.
• If all zones are unstructured, the ΔQ limiter is on.
• If there is a mix of structured and unstructured zones, and CFL# AUTOMATIC is not used in any zone, the ΔQ limiter is off.
• If there is a mix of structured and unstructured zones, and CFL# AUTOMATIC is used in any zone, the ΔQ limiter is on.

Note that although the DQ LIMITER keyword has separate options for structured and unstructured zones, it is not zonal-dependent. The limiter is either off in all zones (both structured and unstructured), or on in all zones using the default or user-specified limits.

Structured Grids

For structured grid zones, the keyword limits the solution by specifying limits on the change in density and/or temperature over a single iteration. The following options apply to structured grid zones.

OFF Don't limit the solution. Use the MacCormack ΔQ limiter. [MacCormack, R. W., "Considerations for Fast Navier-Stokes Solvers", presented at the conference on Advances of Flow Simulation Techniques, Davis, CA, May 1997.] With this limiter, the entire solution, including the turbulence variables, is limited throughout the zone, such that the specified fractional changes in density and temperature are not exceeded. (See below for some further considerations when multiple sub-iterations are being used.) Use the pointwise ΔQ limiter from the NXAIR code. This limiter seeks to ensure that density remains positive, mass fractions remain non-negative, the total energy (without heat of formation) remains positive, and the velocity is not allowed to grow so large that the sensible energy becomes negative. The advantage of this limiter is that it acts locally and does not slow changes in the entire zone. The solution is limited only at those points that exceed the specified fractional changes in density or temperature. Unlike the MacCormack limiter, this limiter is not applied to the turbulence model equations (although the models of course use the limited Navier-Stokes variables, so there is an indirect influence). drmax specifies the fractional change allowed in the density over an iteration. I.e., specifying "DQ LIMITER ON DRMAX 0.2" means the density will not be permitted to change by more than ±20% from one iteration to the next. The default value is 0.5. dtmax specifies the fractional change allowed in the temperature over an iteration. The default value is 0.5. dpmax specifies the fractional change allowed in the pressure over an iteration. The default value is 0.1. Specifies whether limiter messages should be written to the .lis list output file. The default is to print messages.

If just DQ LIMITER is specified, without specifying any options, the MacCormack ΔQ limiter is used. Since the defaults for drmax and dtmax are both 0.5, both density and temperature will be allowed to change by no more than ±50% over an iteration.

The use of DQ LIMITER ON becomes somewhat problematic when multiple sub-iterations are used for the Navier-Stokes equations (using the NAVIER-STOKES ITERATIONS keyword) and/or the turbulence model equations (using the ITERATIONS option with the TURBULENCE keyword). By default, the number of sub-iterations for both the Navier-Stokes and turbulence model equations is one. In this case, each iteration for the Navier-Stokes equations is followed by an iteration for the turbulence model equations, and if the limiter is applied to the Navier-Stokes solution, it is also applied to the turbulence model solution.

If the number of Navier-Stokes sub-iterations is one, and if multiple sub-iterations are used for the turbulence model equations, when the limiter is applied to the Navier-Stokes solution it is applied to each turbulence model sub-iteration.

Also, if multiple Navier-Stokes sub-iterations are used, it's possible that the computed flow field is such that the limiter is applied during some sub-iterations, but not others. In this case, if the limiter is applied during the final Navier-Stokes sub-iteration, it is again applied to each turbulence model sub-iteration. If the limiter is not applied during the final Navier-Stokes sub-iteration, it will not be applied at all during the turbulence model iteration.

For these reasons, it is recommended that the number of sub-iterations for the Navier-Stokes and turbulence model equations be left at their default values of one when the DQ LIMITER is used.

Application of the DQ LIMITER to points on coupled boundaries is controlled by the BC LIMITER keyword, which has a default setting of BC LIMITER OFF.

Unstructured Grids

For unstructured grid zones, the keyword limits the solution by specifying a relaxation factor, and a limit on the change in pressure over a single iteration. The following options apply to unstructured grid zones.

OFF Don't limit the solution. Apply the ΔQ limiter using the default or user-specified limits. dplim specifies the maximum allowable change in pressure, as a fraction of the local pressure, over an iteration. I.e., specifying "DQ LIMITER ON DPMAX 0.2" means the solution will be limited such that the pressure doesn't change by more than 20% from one iteration to the next. The default is 0.1. Relaxation factor. The default is 1.0 if a first-order explicit operator (specified by the RHS keyword) is being used in all zones, and 0.5 otherwise. Specifies whether limiter messages should be written to the .lis list output file. The default is to print messages.

If the DQ LIMITER keyword is used, but without specifying OFF or ON, the ΔQ limiter is on.

When the ΔQ limiter is off, no solution limiting is done. When it's on, the entire solution, including the turbulence solution, is always limited using the relaxation factor dqrlx. In addition, the Navier-Stokes and chemistry solution is limited such that the density changes by no more than 50% over an iteration, and the pressure changes by no more than the amount specified using the DQ LIMITER keyword. And the turbulence solution is limited such that the turbulence variables change by no more than 50% over an iteration.

DQ LIMITER OFF may not be specified if CFL# AUTOMATIC is used in any zone.