Theory

The compressible solver updates the density from the equation of state after each pressure correction. Like the pressure, the density is relaxed as a FIELD, equation (1): only the fraction $\alpha_\rho$ of the change is kept. With the subsonic pressure equation (transonic false) the density in the mass fluxes is that of the previous iteration; a large density change between iterations then feeds back into the pressure, which is why plain SIMPLE relaxes the density strongly.

On auto the value moves with the pressure relaxation:

0.1 with plain SIMPLE (the compressible auto choice);
1.0 when SIMPLEC is applied (a typed pressure relaxation with SIMPLEC on) and with the transonic SIMPLE solver;
the pseudo-transient solver relaxes nothing.

Full table: Pressure relaxation.

Equations

\rho^{n+1} = \rho^{n} + \alpha_\rho\left(\rho^{*} - \rho^{n}\right), \qquad \rho^{*} = \frac{p^{n+1}}{R_s T}

(1)

where	meaning	unit
$\rho^{n}$	Density of the previous iteration	kg/m³
$\rho^{*}$	Density from the equation of state with the new pressure	kg/m³
$R_s$	Specific gas constant	J/(kg K)
$T$	Temperature	K
$\alpha_\rho$	Density relaxation factor	-

Default and rule

Default: auto: 0.1 (compressible SIMPLE), 1.0 (SIMPLEC with a typed p, transonic SIMPLE)Computed by the programMeasured
Rule: Auto: 0.1 for the compressible SIMPLE solver (also after a divergence fallback); 1.0 with SIMPLEC or transonic SIMPLE.
Source: Validation on case V1 (a 2.0 m multi-chamber muffler with a perforated pipe and three absorptive packings; the compressible solver, 691k cells): under SIMPLEC, changing $\alpha_\rho$ from 1.0 to 0.01 changed nothing (identical abort in iteration 3); plain SIMPLE with $\alpha_\rho = 0.1$ , $\alpha_p = 0.3$ ran. The transonic value 1.0 is that of OpenFOAM's squareBend tutorial. Field relaxation in SIMPLE: (Patankar and Spalding, 1972).

Valid range 0 < α ≤ 1; compressible only

Values

$0 < \alpha_\rho \le 1$ . Used only by the compressible SIMPLE solvers.

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; compressible only

Related 3

References 1