Δp mean-stability tolerance

simulation_control.dp_plateau.tolerance_pct Unit: % Step 07 · Run Settings

The criterion that stops a steady run and decides quality gate 2's pressure-drop check: the run has converged when the mean of the total-pressure drop over the averaging window no longer drifts and its three block means agree, both within this percentage of the mean.

Last updated 2026-11-03

Theory

The total-pressure drop $\Delta p_0$ (mass-flow weighted, inlets minus outlets) is evaluated every iteration. A steady RANS solution with jets often keeps oscillating by 5-30 % peak to peak for ever while its mean is stable; a test on the noise of the signal would never pass, so the program tests the mean.

From the samples after the start-up phase and the settle iterations (Upwind iterations before the switch), the most recent $W$ (Δp window) are first searched for a dominant oscillation period $P$ (the autocorrelation of the linearly detrended signal, a peak of at least 0.3 at a lag of 2 or more). The window is widened to $N = \max(W, 2P)$ , so at least two full periods are averaged. The run is converged when both the linear drift across the window, equation (1), and the largest deviation of its three block means from the window mean, equation (2), are within $\varepsilon$ . Drift catches a monotone trend; the block spread catches a slower wander that the straight-line fit averages away.

While the solver runs, the program checks this every few seconds; once it is met it sets stopAt writeNow and the solver writes its fields and ends. The reported pressure drop is the window mean, quoted with the larger of $\varepsilon$ and the measured uncertainty, equation (3), which uses the integrated autocorrelation time because successive samples are not independent. When the coefficient of variation of the window exceeds 3 %, the converged mean is flagged "unsteady" (a limit cycle; not a failure).

A transient run uses this tolerance, but not below 1 %, for the comparison of the last two averaging windows (Time dependency).

Equations

\delta_{drift} = \frac{\lvert s\rvert N}{\lvert\bar{x}\rvert} \le \varepsilon

(1)

\delta_{block} = \frac{\max_{j=1,2,3}\lvert\bar{x}_j - \bar{x}\rvert}{\lvert\bar{x}\rvert} \le \varepsilon

(2)

u = \frac{2\sigma}{\sqrt{N/\tau_{int}}\,\lvert\bar{x}\rvert}, \qquad \tau_{int} = 1 + 2\sum_{k \ge 1,\ \rho_k > 0}\rho_k

(3)

where	meaning	unit
$\bar{x}$	Mean of $\Delta p_0$ over the window of $N$ samples	Pa
$s$	Slope of the least-squares line through the window	Pa per iteration
$N$	Window length, $\max(W, 2P)$	iterations
$\bar{x}_j$	Mean of the $j$ -th third of the window	Pa
$\varepsilon$	Tolerance (this setting)	%
$\sigma$	Standard deviation of the window	Pa
$\tau_{int}$	Integrated autocorrelation time (summed while the autocorrelation $\rho_k$ stays positive)	iterations
$u$	Measured uncertainty of the mean	%

Default and rule

Default: 0.5 % (transient: at least 1 %)Measured
Rule: 0.5 %.
Source: The rule tests the mean because two simpler rules fail on muffler flows: a window-to-window plateau rule stops benign runs 2-4 % off and "converges" oscillating muffler runs by coincidence, and a noise (coefficient-of-variation) test is never passed by a limit cycle. On the study mufflers the last-iteration values were 4257 / 4121 / 5048 Pa against window means of 4230-4500 Pa on three meshes. Finite-sample caveat: a straight-line fit to an exactly periodic signal shows a small artificial drift (about 1.5 % at 20 samples, 0.06 % at 500), which is why the window should be long. The integrated autocorrelation time uses the standard estimator for correlated series.

Valid range > 0; 0 never converges (no automatic stop, gate 2 not met)

Values

Above 0. Smaller is stricter and needs more iterations.

Zero

0 can never be met: there is then no automatic stop, the run goes to the maximum number of iterations, and gate 2 reports the pressure drop as not converged.

Theory

Equations

Default and rule

Valid range > 0; 0 never converges (no automatic stop, gate 2 not met)

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