IMPLICIT {word1 [word2 word3 [zone_selector [tre]]] | \
          JACOBI jiter jcnv [RELAX jrel] [zone_selector] | \
          GAUSS giter gcnv [RELAX grel] [zone_selector] | \
          MACCORMACK [MAFK k] [zone_selector] | \
          OVERFLOW [zone_selector]}

This keyword allows user control of the implicit operator within each zone. There are five possible modes, defined as follows:

IMPLICIT word1 [word2 word3 [zone_selector [tre]]]

This form of the the IMPLICIT keyword allows the user to turn off the implicit operator completely, resulting in an explicit calculation, or to use a scalar or full block implicit operator. With these options, a different implicit operator may be specified for each computational direction.

The user-specified parameters are defined as follows:

	word1		A keyword controlling the xi-direction implicit operator
	word2		A keyword controlling the eta-direction implicit operator
	word3		A keyword controlling the zeta-direction implicit operator
	tre		Specifies the trapezoidal time differencing factor. The possible values are:     0    Explicit (but expensive, don't use) 1 or omitted    Implicit 0.5    Trapezoidal time differencing

The keywords that may be used for word1, word2, and word3 are defined in the following table.

	Keyword		Difference Scheme
	NONE		Explicit
	SCALAR		Scalar implicit operator (default for Euler solutions)
	FULL		Full block implicit operator (default for viscous solutions)

Note that if only one of the above keywords is specified, WIND assumes that the specified operator is to be used in all directions in all zones.

IMPLICIT JACOBI jiter jcnv [RELAX jrel] [zone_selector]

This form of the IMPLICIT keyword turns on the point Jacobi implicit operator in the selected zone. The user-specified parameters are defined as follows:

	jiter		The number of subiterations allowed each time step. A typical value is 30.
	jcnv		The level of convergence to assume the subiterations are converged. A typical value is 0.0001.
	jrel		The relaxation factor. The default value is 1.0 (i.e., no relaxation).

IMPLICIT GAUSS giter gcnv [RELAX grel] [zone_selector]

This form of the IMPLICIT keyword turns on the Gauss-Seidel implicit operator in the selected zone. The user-specified parameters are defined as follows:

	giter		The number of subiterations allowed each time step. A typical value is 10.
	gcnv		The level of convergence to assume the subiterations are converged. A typical value is 0.0001.
	grel		The relaxation factor. The default value is 1.0 (i.e., no relaxation).

IMPLICIT MACCORMACK [MAFK k] [zone_selector]

This form of the IMPLICIT keyword turns on MacCormack's first-order modified approximate factorization (MAFk) procedure in the selected zone. The procedure attempts to remove the decomposition error by feeding the error term back into the matrix equations on the right-hand side.

The solution process requires subiterations, with the number of subiterations specified with the MAFK option by the parameter k. The default for k is 2.

For stability, the IMPLICIT BOUNDARY keyword should be used to specify that implicit boundary conditions are to be used with the MAFk procedure. In addition, when large CFL numbers are to be used, it is recommended that the CFL number be increased gradually (over 200 iterations or so) to the desired value using the INCREMENT parameter in the CFL# keyword.

The MAFk procedure has been demonstrated in WIND to be stable in two dimensions with very high CFL numbers (greater than 1000). In three dimensions, however, only limited testing has been done, and its efficiency has not yet been determined.

IMPLICIT OVERFLOW [zone_selector]

This form of the IMPLICIT keyword specifies that the "ARC3D 3-factor diagonal scheme" as implemented in OVERFLOW 1.8q is to be used. Tests indicate that this scheme is faster than the other implicit schemes, and gives comparable answers.

This option is currently available only for 3-d perfect gas flows, with explicit boundary conditions. It also uses more memory than the other implicit schemes, due to the interface coding used to implement it in the WIND code.

See Also: IMPLICIT BOUNDARY