Non repeatability issue

Aldo Bonfiglioli aldo.bonfiglioli at
Tue Mar 18 08:48:27 CDT 2008

> 1) You have way too many Newton steps. Newton is quadratically
>convergent, so if
>      you have 100+ steps, it means you are very very far from the
>solution when you
>      begin. In this region, Newton is a really bad algorithm and can
>be very very
>      sensitive to perturbations. I would never expect it to be
>reproducible. From the
>      well-known fracint demo, it can be chaotic.

The initial solution from which Newton's algorithm is started
is obtained using a fixed point iterative scheme in which the
turbulence transport eqn is solved de-coupled
from the mean-flow eqns.
This de-coupled solution strategy usually stalls (in terms of residual
decrease) after a residual drop of a few orders of magnitude.
At this stage Newton is invoked.
 From a qualitative view-point (say at plotting level)
the initial solution is close to the fully converged one, but
I will try to quantify this and check how mutually far or close are the two.
Even for the 2D RANS eqns we have noticed a fairly "long"
plateau in terms of residual convergence history before
quadratic convergence occurs. This is also in line with
the few references on the subject I have in mind.
3D Euler is far more benign in our experience.

>  2) I would also question whether the system is actually stable.
>Instability can result
>      in occasional divergence based upon small perturbations.
We know this might occur. At this stage we are still
trying to make sure there are no implementation bugs
in our code.


Dr. Aldo Bonfiglioli di Ingegneria e Fisica dell'Ambiente (DIFA)
Universita' della Basilicata
V.le dell'Ateneo lucano, 10 85100 Potenza ITALY
tel:+39.0971.205203 fax:+39.0971.205160

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