Linear Pressure-Strain Model

The linear model of Gibson and Launder [339] for the pressure-strain term comprises five terms; these are the rapid term, the slow (return-to-isotropy) term, and their respective wall-reflection terms:

The slow pressure-strain term ${\underline{\varphi }}_s$ is modeled as:

where:

• $C_1$ is a Model Coefficient.
• $\rho$ is the density.
• $k$ is the turbulent kinetic energy given by Eqn. (1313).
• $I$ is the identity tensor.

The rapid pressure-strain term ${\underline{\varphi }}_r$ is modeled as:

where:

• $C_2$ is a Model Coefficient.
• $\mathbf{\text{P}}$ is given by Eqn. (1315).

The buoyancy contribution ${\underline{\varphi }}_{r,b}$ is modeled as:

where:

• $C_3$ is a Model Coefficient.
• $\mathbf{\text{G}}$ is given by Eqn. (1316).

The slow wall-reflection term ${\underline{\varphi }}_{1w}$ is modeled as:

where:

• $C_{1w}$ is a Model Coefficient.
• $\mathbf{\text{N}}=\mathbf{\text{n}}\otimes \mathbf{\text{n}}$ , where the “wall-normal unit vector” $\mathbf{\text{n}}$ is defined as the normalized gradient of the wall distance.

$f_w$ is calculated as:

where:

• $C_l$ and $f_w^{\text{max}}$ are Model Coefficients.
• $d$ is the distance to the wall.

The rapid wall-reflection term ${\underline{\varphi }}_{2w}$ is modeled as:

where $C_{2w}$ is a Model Coefficient.

Model Coefficients

$C_1$	$C_2$	$C_{1w}$	$C_{2w}$	$C_3$	$C_l$	$f_w^{\max }$
1.8	0.6	0.5	0.3	0.5	2.5	1