Theory

With Per-field residual tolerances on, gate 2 judges each of the three velocity components $U_x$ , $U_y$ and $U_z$ separately against this tolerance. 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).

Velocity and pressure are the slowest to converge where jets leave tubes and holes; on the study mufflers their initial residuals held at $10^{-2}$ to $10^{-3}$ while the pressure drop was stable.

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_{U} \ \ \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 \{U_x, U_y, U_z\}

(1)

where	meaning	unit
$r_{\phi,i}$	Initial residual of field $\phi$ at iteration $i$	-
$r_{U}$	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

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