Theory

With Per-field residual tolerances on, gate 2 judges the pressure $p$ against this tolerance; a solver that names the field $p_{rgh}$ is mapped to the same tolerance. The test is that of Residual target, equation (1): either the largest initial residual over the last 50 iterations is below the tolerance, or the residual has fallen by the residual drop (Residual drop) since the start of the run.

The pressure equation carries the continuity constraint. Its residual is usually the highest of a muffler run and the first to stall.

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 (its own residualControl stays at $10^{-5}$ ); it decides only whether gate 2 reports the residuals as converged.

Equations

\max_{i \in \text{last 50}} r_{\phi,i} < r_{p} \ \ \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 \{p\}

(1)

where	meaning	unit
$r_{\phi,i}$	Initial residual of field $\phi$ at iteration $i$	-
$r_{p}$	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 established by measurement. The auto value is the single residual target, whose basis is the residual-sensitivity study described in Residual target.

Valid range 0 < r < 1

Values

Between 0 and 1 (exclusive), or auto.

References 1

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

Theory

Equations

Default and rule

Valid range 0 < r < 1

Related 3

References 1