Theory

The compressible solver solves the energy equation for the sensible internal energy $e$ ; the temperature follows from $e$ and the heat-capacity model, and the density from the temperature and pressure. The equation is relaxed implicitly, equation (1), in the same way as momentum. With heat transfer the wall heat loss makes the energy equation the slowest to converge. The program then also waits for the energy balance (enthalpy lost by the gas against heat through the walls, within 1 %) before it stops on a converged pressure drop.

Auto values:

0.7 for a flow-only compressible run.
0.9 when SIMPLEC is applied and heat transfer is solved. Because the compressible auto set is plain SIMPLE, 0.9 is reached only with a typed pressure relaxation and SIMPLEC on.
0.8 with the transonic SIMPLE solver.
The pseudo-transient solver relaxes nothing.

Full table: Pressure relaxation.

Equations

\frac{a_P}{\alpha_e}\,e_P = \sum_{nb} a_{nb}e_{nb} + b + \frac{1-\alpha_e}{\alpha_e}\,a_P\,e_P^{old}

(1)

where	meaning	unit
$e_P$	Sensible internal energy of cell P	J/kg
$e_P^{old}$	Value of the previous iteration	J/kg
$a_P, a_{nb}$	Diagonal and neighbour coefficients of the energy matrix	kg/s
$b$	Source terms (pressure work, kinetic energy, heat flux)	W
$\alpha_e$	Relaxation factor	-

Default and rule

Default: auto: 0.7; 0.9 with SIMPLEC and heat transfer; 0.8 (transonic SIMPLE)Computed by the program
Rule: Auto (see above). A typed value is used as typed.
Source: 0.7 is the program's long-standing value for the compressible energy equation; it keeps flow-only compressible results reproducible. 0.9 with SIMPLEC and heat transfer is a program choice; the heat-transfer validation (insulated pipe, energy balance 0.017 %) was made with it under SIMPLEC, not with the current plain-SIMPLE compressible auto set. 0.8 is the value of OpenFOAM's squareBend tutorial. Implicit relaxation: (Patankar and Spalding, 1972).

Valid range 0 < α ≤ 1; compressible only

Values

$0 < \alpha_e \le 1$ . 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 5

References 1