Linear Pressure-Strain Model

The linear model of Gibson and Launder [46] for the pressure-strain term comprises four terms; these are the rapid part, the slow part, and their respective wall-reflection terms:

(303)

The slow pressure-strain term is modeled as:

(304)

The rapid pressure-strain term is modeled as:

(305)

The slow wall-reflection term is modeled as:

(306)

where:

(307)

is the wall distance and the tensor is given by:

(308)

and the "wall-normal unit vector" is defined as the negative of the wall direction.

The rapid wall-reflection term is modeled as:

(309)

Two possible sets of coefficients are used. In the event that wall functions are used, (that is, no two-layer model) they have the following constant values:

(310)

In the event that the two-layer model is used, the first four coefficients are expressed in terms of the turbulent Reynolds number and anisotropy tensor as recommended by Launder and Shima [47]:

(311)

(312)

(313)

(314)

(315)

The parameter and the tensor invariants and are defined as:

(316)

(317)

(318)

where the anisotropy tensor is defined as:

(319)