Theory

The $\omega$ equation of the SST model (Turbulence model) is relaxed implicitly, equation (1), in the same way as the $k$ equation (Turbulent kinetic energy relaxation). Near walls $\omega$ is very large (the wall function sets it in the first cell) and varies by orders of magnitude; relaxation keeps the eddy viscosity $\nu_t = a_1 k/\max(a_1\omega, b_1 F_2 S)$ from jumping between iterations.

The auto values for every solver are in the table of Pressure relaxation.

Equations

\frac{a_P}{\alpha_\omega}\,\omega_P = \sum_{nb} a_{nb}\omega_{nb} + b + \frac{1-\alpha_\omega}{\alpha_\omega}\,a_P\,\omega_P^{old}

(1)

where	meaning	unit
$\omega_P$	Specific dissipation rate of cell P	1/s
$\omega_P^{old}$	Value of the previous iteration	1/s
$a_P, a_{nb}$	Diagonal and neighbour coefficients of the $\omega$ matrix	m³/s
$b$	Source terms	m³/s²
$\alpha_\omega$	Relaxation factor	-

Default and rule

Default: auto: 0.7 (SIMPLEC and plain SIMPLE), 0.9 (transonic SIMPLE)Computed by the programMeasured
Rule: Auto: 0.7 with SIMPLEC and with plain SIMPLE; 0.9 with the transonic SIMPLE solver; not relaxed by the pseudo-transient solver; 0.7 after a divergence fallback.
Source: The same validation runs as for $k$ (two-inlet test muffler, Pressure relaxation); $k$ and $\omega$ were always varied together. Implicit relaxation: (Patankar and Spalding, 1972).

Valid range 0 < α ≤ 1

Values

$0 < \alpha_\omega \le 1$ . Keep it equal to the relaxation of $k$ unless there is a reason not to.

References 1

Patankar, S. V. and Spalding, D. B. (1972). A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15(10), 1787-1806. DOI 10.1016/0017-9310(72)90054-3

Theory

Equations

Default and rule

Valid range 0 < α ≤ 1

Related 4

References 1