The objective of Wind-US's convergence acceleration scheme is to approach the steady state solution more quickly by allowing the use of a large CFL number early in the calculation, adding smoothing to maintain numerical stability. This option should be used in conjunction with the SMOOTHING keyword.

Structured Grids

The ZONE keyword identifies the zone within which convergence acceleration is to be used. If convergence acceleration is to be used in multiple zones, and/or if different starting and ending iteration values are to be used in different zones, multiple ZONE keywords must be specified.

iter₁ and iter₂ specify starting and ending iteration values for varying the corresponding keyword parameter. If these aren't specified, the following default values are used.

	Option		iter1		iter2
	SECOND		1		150
	FOURTH		50		500
	CFLRAMP		50		500

The CFL number will be ramped down linearly from its starting value, specified using the CFL# keyword, to 1.0. The ACCELERATE keyword does not work when CFL# MODE 3 (i.e., the time step calculation procedure from OVERFLOW) is used.

The smoothing that is applied depends on the mode used with TEST option 49, and the input from the SMOOTHING and/or BOUNDARY-DAMP keywords. For the second-order smoothing,

	mode		Second-Order Smoothing
	< 2		Smoothing varies with iteration i, as follows: i ≤ iter1    Smoothing applied as determined by the SMOOTHING keyword iter1 < i < iter2 Smoothing coefficient decreased linearly to 0 i ≥ iter2 No smoothing applied
	2		Smoothing varies with iteration i, as follows: i ≤ iter1    Smoothing applied as determined by the SMOOTHING and/or BOUNDARY-DAMP keywords iter1 < i < iter2 Smoothing coefficient decreased linearly to 0 i ≥ iter2 No smoothing applied
	3		No smoothing applied

And for the fourth-order smoothing,

	mode		Fourth-Order Smoothing
	< 2		Smoothing applied as determined by the SMOOTHING keyword
	2		Smoothing varies with iteration i, as follows: i ≤ iter1    No smoothing applied iter1 < i < (iter1 + iter2) / 2 Smoothing coefficient increased linearly from 0 to value determined by the SMOOTHING and/or BOUNDARY-DAMP keywords (iter1 + iter2) / 2 < i < iter2 Smoothing coefficient decreased linearly to 0 i ≥ iter2 No smoothing applied
	3		Smoothing applied as determined by the SMOOTHING and/or BOUNDARY-DAMP keywords

Recommended values for the second- and fourth-order smoothing parameters val₁ and val₂ specified with the SMOOTHING keyword, and for the starting CFL number, are:

	Dimensions		val1		val2		CFL #
	2D		0.1		0.03		10-15
	3D		0.06		0.01		2.5

Example

In the following example, convergence acceleration is applied in zones 3 and 4. Second-order smoothing is applied between iterations 1 and 200, and fourth-order smoothing is applied between the default values of iterations 50 and 500. The CFL number specified with the CFL# keyword will be used for the first 250 iterations, then ramped down to a value of 1.0 between iterations 250 and 500.

   SMOOTHING SECOND 0.06 FOURTH 0.01 SMLIMT 0.
   ACCELERATE
      ZONE 3
      ZONE 4
      SECOND START 1 END 200
      CFLRAMP START 250 END 500
   ENDACCELERATE
   TEST 49 2

Unstructured Grids

The ZONE keyword identifies the zone within which convergence acceleration is to be used. If convergence acceleration is to be used in multiple zones, and/or if different starting and ending iteration values are to be used in different zones, multiple ZONE keywords must be specified.

iter₁ and iter₂ specify starting and ending iteration values for varying the CFL number. Just as for structured grids, for unstructured grids the CFL number will be ramped down linearly from its starting value, specified using the CFL# keyword, to 1.0. If the CFLRAMP keyword isn't specified, default values of 50 and 500 are used, for iter₁ and iter₂.

For unstructured grids, however, no variation in smoothing is done. The smoothing specified with the SMOOTHING keyword is used for all iterations.

See Also: SMOOTHING, CFL#