Upwind iterations before the switch

numerics.turbulence_upwind_iterations Unit: iterations Step 06 · Solver Settings

The length of the first-order start-up phase of a steady run. For this many iterations $k$ and $\omega$ are convected with first-order upwind; the solver is then restarted with the final schemes and relaxation.

Last updated 2026-11-03

Theory

A steady run consists of two solver invocations.

1. Phase 1 (iterations 1 to $N_{up}$ ) uses first-order upwind for $k$ and $\omega$ (bounded Gauss upwind; the plain form for the pseudo-transient solver). The transonic SIMPLE and pseudo-transient compressible solvers also use it for U and energy. The phase uses the start-up velocity relaxation and, for the pseudo-transient solver, the start-up Courant number. A full field set is written at its last iteration. 2. Phase 2 restarts from that field set with the scheme of k and ω convection scheme, the final velocity relaxation (Velocity relaxation) and the final Courant number.

The switch is a real restart with the dictionaries edited in place, not a scheme switched at run time, because the installed OpenFOAM build cannot compile code.

A restart disturbs the solution: on a real muffler the first iteration after it showed a pressure residual of about 0.4, a continuity error about 18 times higher than before, and a pressure drop 17 % off for about 40 iterations. The convergence rule therefore does not use the pressure-drop samples of phase 1 or of the disturbed stretch after the restart (the settle iterations), equation (1).

Each time it judges convergence, the program finds the end of the disturbance from the pressure drop itself with the Marginal Standard Error Rule on batch means of 5 samples (MSER-5), equation (2). It removes the stretch whose removal makes the mean of the remaining samples most precise.
With perforated tubes whose loss coefficient follows the flow, a later restart for a changed coefficient moves the start further.

The upwind phase also counts in the automatic iteration budget (Maximum iterations). A run paused inside it cannot be continued.

Equations

i_{start} = \max\!\left(N_{up},\ i_{restart}\right) + N_{settle} \qquad (1)

(1)

N_{settle} = 5\,d^{*}, \qquad d^{*} = \arg\min_{0 \le d \le b/2} \frac{1}{(b-d)^2} \sum_{j=d+1}^{b} \left(Z_j - \bar Z_{d}\right)^2 \qquad (2)

(2)

where	meaning	unit
$i_{start}$	First iteration whose pressure-drop sample counts for convergence	-
$N_{up}$	Upwind iterations (this setting), capped at the maximum number of iterations	-
$i_{restart}$	Iteration of the last restart made for a perforate loss update (if any)	-
$N_{settle}$	Settle iterations after a restart, found by equation (2)	-
$Z_j$	Mean of the j-th batch of 5 pressure-drop samples after the restart	Pa
$b$	Number of batches so far	-
$\bar Z_{d}$	Mean of the batches after the first d	Pa

Default and rule

Default

200

Rule

200 iterations. With 0, or with $N_{up}$ at or above the maximum number of iterations, there is only one phase.

Source

The two-phase start is the program's convention for robustness of $k$ and $\omega$ near the jets during the crude first iterations; it is not taken from a publication. The restart disturbance described above was measured on the two-baffle test muffler.

Settle iterations: MSER (White, 1997), used as MSER-5, the variant found most effective and robust in a comparison of five truncation rules (White, Cobb and Spratt, 2000). The search covers the first half of the samples (the method's assumption "n >> d"); a minimum at the end of that half means the disturbance has not died out yet. The stretch is capped at 300 iterations: once 300 samples have run since the restart, at most 300 are removed. Validation results: on the two-baffle test muffler the settle stretch ends 60 iterations after the restart; on a V5 muffler with no visible disturbance nothing is removed, and the run converges at iteration 385 instead of 669 with a fixed 300-iteration stretch (means 0.4 % apart). OpenFOAM restart mechanics: (OpenFOAM user guide, 2026).

Valid range ≥ 0

Values

Any whole number ≥ 0. Larger values give a more established field at the switch and a longer run.

Transient

Transient runs have no start-up phase: they use first-order $k$ and $\omega$ convection throughout.

Theory

Equations

Default and rule

Valid range ≥ 0

Related 5

References 3