Theory

With Per-field residual tolerances on, gate 2 judges the energy equation, whether the solver prints it as $e$ (sensible internal energy, the form used here) or $h$ . The test is the one of Residual target: the largest initial residual over the last 50 iterations must be below this tolerance, or the residual must have fallen by the residual drop (Residual drop) from the start of the run, equation (1).

With heat transfer the energy equation is the slowest to settle; the run then also waits for the energy balance (gas enthalpy loss against wall heat, within 1 %) before it stops.

The residual is OpenFOAM's normalised initial residual (OpenFOAM user guide, 2026): dimensionless, whatever the unit of the field. The tolerance never stops the solver itself (its own residualControl stays at $10^{-5}$ ); it decides whether gate 2 reports the residuals as converged.

Equations

\max_{i \in \text{last 50}} r_{\phi,i} < r_{e} \ \ \lor\ \ \log_{10}\frac{\max_{i \le 10} r_{\phi,i}}{\max_{i \in \text{last 50}} r_{\phi,i}} \ge D, \qquad \phi \in \{e\}

(1)

where	meaning	unit
$r_{\phi,i}$	Initial residual of field $\phi$ at iteration $i$	-
$r_{e}$	Tolerance of this equation (this setting)	-
$D$	Residual drop, when set	decades

Default and rule

Default: auto (= the residual target: 1e-3 steady)Computed by the program
Rule: Auto: the single residual target ( $10^{-3}$ for a steady run). A typed value is used only while per-field tolerances are on.
Source: No separate default per equation has been measured; the auto value is the single target, whose basis is the program's residual-sensitivity study (see Residual target).

Valid range 0 < r < 1; compressible only

Values

Between 0 and 1 (exclusive), or auto. Shown for compressible runs only.

References 1

OpenCFD Ltd. (2026). OpenFOAM user guide. openfoam.com. Web page

Theory

Equations

Default and rule

Valid range 0 < r < 1; compressible only

Related 3

References 1