Wind-US User's Guide - Keyword Reference, TVD

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TVD - Total Variation Diminishing operator flag

Structured Grids

TVD [OFF | FACTOR factor | MINMOD [factor] | KOREN [factor] | ALBADA] \ [zone_selector]

Unstructured Grids

TVD [OFF | FACTOR factor | MINMOD [factor] | SUPERBEE factor | \ VENKAT [factor [KVENKAT K_Venk]]] [zone_selector]

Structured Grids

For structured grids, this keyword controls the TVD flux limiter in the explicit operator, which is helpful in preventing overshoots in flowfield properties in regions of high gradients. TVD may be used with the Coakley, Roe, Van Leer, HLLE, and Rusanov explicit schemes. TVD is enabled by default for these schemes, using the standard minmod TVD limiter with the default compression parameter, and disabled for all others.

OFF Disables TVD for the specified zone(s)

FACTOR Use the standard minmod TVD limiter. The value of factor specifies the "compression" parameter for the TVD algorithm, which controls the amount of limiting applied.

MINMOD Use the standard minmod TVD limiter. This is the same as FACTOR, except that the factor may be defaulted. The value of factor specifies the "compression" parameter for the TVD algorithm, which controls the amount of limiting applied. The default compression parameter is the maximum value which assures TVD properties for the explicit operator being used (as specified by the RHS keyword). The default values are shown in the following table for the various versions of the explicit differencing scheme.

Explicit Operator factor
First-order, upwind 0 (i.e., not applicable)
First-order, upwind, modified for stretched grids 2
Second-order fully upwind 2
Second-order central 2
Second-order upwind-biased 3
Second-order upwind-biased, modified for stretched grids 3
Third-order upwind-biased 4
Third-order fully upwind Not available
Fourth- and fifth-order Not available

KOREN Use the Koren TVD limiter. With this limiter, the default value of factor is 1.0, and does not depend on the explicit operator being used.

ALBADA Use the van Albada TVD limiter. With this limiter, no factor value is input.

If TVD flux limiting is turned on for an invalid explicit scheme, an error message is generated and the run will abort. If TVD flux limiting is turned on for a valid scheme, but with third-order fully upwind, fourth-order, or fifth-order differencing, TVD flux limiting is automatically disabled and the run will continue.

See Also: BOUNDARY TVD, RHS

Unstructured Grids

For unstructured grids, standard slope limiting is performed by default for all viscous cases, and for inviscid cases with second-order spatial differencing specified with the RHS keyword.

OFF Disables slope limiting for the specified zone(s)

FACTOR Use the standard slope limiting procedure. The value of factor specifies the slope limiting parameter, and must be specified.

MINMOD Use the standard slope limiting procedure. This is the same as FACTOR, except that the factor may be defaulted. The default slope limiting parameter is 0.0 for first-order spatial differencing, and 3.0 for second-order differencing.

SUPERBEE Use "super-bee" slope limiting. The slope limiting parameter factor must be specified.

VENKAT Use Venkatakrishnan slope limiting. [Venkatakrishnan, V., "Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters," Journal of Computational Physics, Vol. 118, 1995, pp. 120-130.] A value of 3.0 for the slope limiting parameter factor corresponds to second-order, and 0.0 corresponds to first-order. Values between 0.0 and 3.0 result in linear interpolation between the first-order and second-order face states. The default (and maximum allowed) value for factor is 3.0.
The optional K_Venk specified using KVENKAT is a coefficient determining the value of a "knob" that controls the allowable amount of oscillation. The value is set to K_Venk D_cell, where D_cell is the diameter of a sphere with the same volume as the current cell. The default for K_Venk is 20.

See Also: RHS

	`OFF`		Disables slope limiting for the specified zone(s)
	`FACTOR`		Use the standard slope limiting procedure. The value of factor specifies the slope limiting parameter, and must be specified.
	`MINMOD`		Use the standard slope limiting procedure. This is the same as `FACTOR`, except that the factor may be defaulted. The default slope limiting parameter is 0.0 for first-order spatial differencing, and 3.0 for second-order differencing.
	`SUPERBEE`		Use "super-bee" slope limiting. The slope limiting parameter factor must be specified.
	`VENKAT`		Use Venkatakrishnan slope limiting. [Venkatakrishnan, V., "Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters," Journal of Computational Physics, Vol. 118, 1995, pp. 120-130.] A value of 3.0 for the slope limiting parameter factor corresponds to second-order, and 0.0 corresponds to first-order. Values between 0.0 and 3.0 result in linear interpolation between the first-order and second-order face states. The default (and maximum allowed) value for factor is 3.0. The optional K_Venk specified using `KVENKAT` is a coefficient determining the value of a "knob" that controls the allowable amount of oscillation. The value is set to K_Venk D_cell, where D_cell is the diameter of a sphere with the same volume as the current cell. The default for K_Venk is 20.