Theory

The $k$ equation of the SST model (Turbulence model) is relaxed implicitly in the same way as momentum, equation (1): the diagonal is divided by $\alpha_k$ and the old value is carried on the right-hand side, so the converged solution is unchanged. $k$ and $\omega$ are strongly coupled through the eddy viscosity. Too little relaxation lets the eddy viscosity jump between iterations near the jets; too much slows the convergence of the whole system.

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

Equations

\frac{a_P}{\alpha_k}\,k_P = \sum_{nb} a_{nb}k_{nb} + b + \frac{1-\alpha_k}{\alpha_k}\,a_P\,k_P^{old}

(1)

where	meaning	unit
$k_P$	Turbulent kinetic energy of cell P	m²/s²
$k_P^{old}$	Value of the previous iteration	m²/s²
$a_P, a_{nb}$	Diagonal and neighbour coefficients of the $k$ matrix	m³/s
$b$	Source terms (production and part of the dissipation)	m⁵/s³
$\alpha_k$	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 (incompressible and compressible); 0.9 with the transonic SIMPLE solver; not relaxed by the pseudo-transient solver; 0.7 after a divergence fallback.
Source: Validation on the two-inlet test muffler (see Pressure relaxation): with plain SIMPLE, $k$ and $\omega$ at 0.5 gave a lower pressure residual than at 0.7 or 0.3 (2.3e-2 against 7.1e-2 and 4.2e-2 with U 0.5); with SIMPLEC, 0.7 and 0.9 both converged (1.6e-2 and 1.1e-2). The auto value 0.7 is the program's default for both couplings. Implicit relaxation: (Patankar and Spalding, 1972).

Valid range 0 < α ≤ 1

Values

$0 < \alpha_k \le 1$ . Keep $k$ and $\omega$ equal 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