Theory

PIMPLE combines the PISO pressure correctors within a step (Pressure correctors) with SIMPLE-like outer iterations over the whole step (OpenFOAM user guide, 2026):

With one outer corrector it is PISO: the nonlinear coupling within the step is not iterated, which is accurate only at Courant numbers below about 1.
With several, the nonlinearity is iterated within each step, and larger steps remain stable.

The relaxation factors of the Solver Settings step apply to these outer iterations. The last outer corrector of each step is solved with the tight "Final" solver settings (relative tolerance 0).

A step may end its outer correctors early, equation (1): when the initial residuals of pressure and velocity at the start of an outer corrector are already below $10^{-5}$ (outerCorrectorResidualControl). This only saves passes on easy steps; $N_{outer}$ remains the maximum.

Equations

\text{outer loop of step } n \text{ ends when } j = N_{outer}\ \ \lor\ \ \left(r_{p,j} < 10^{-5}\ \land\ r_{U,j} < 10^{-5}\right)

(1)

where	meaning	unit
$j$	Outer-corrector index within the step	-
$N_{outer}$	Outer correctors (this setting)	-
$r_{p,j}, r_{U,j}$	Initial residuals of pressure and velocity at corrector $j$	-

Default and rule

Default: 2Measured
Rule: 2.
Source: Validation runs of the program (residual-sensitivity study): one outer corrector at Courant 5 diverged on every case; 2 outer correctors at Courant 2-3.5 were stable on a pipe and on the mufflers. 2 is the smallest number of outer correctors with which these stable settings were validated.

Valid range 1 to 10

Values

1 to 10. Each outer corrector costs about one more steady iteration per time step.

References 1

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

Theory

Equations

Default and rule

Valid range 1 to 10

Related 3

References 1