open TELEMAC-MASCARET The mathematically superior suite of solvers

Dear Sébastien,

unfortunately after a more thorough examination it occures that wetting and drying algorithms (or their treatment in parallel) cannot be blamed for the differences along the shoreline between runs with different number of mesh partitions. The differences these "tidal flats" algorithms produce are secondary. The real error cause seem to be the instabilities of the free surface which are, unfortunately, intrinsic/inherent to finite element type applied in Telemac-2D. Google for "spurious instabilities in P1-P1 elements". In the eighties of the twentieth century they were very popular and so easy to treat, especially in pre- and postprocessing, but nowadays no-one would seriously develop a program for the shallow water equations using these elements. The main cause of *our* parallel problem is that the P1-P1 element instabilities itself tend to differ in differently partitoned meshes, due to their erratic character.

The bad news is that presently probably no-one would do the titanic work of rewriting the fundamental BIEF library for another computationally efficient, but stable element. The good news is that the instabilities intrinsic to the method can be damped by changing the method the gradients of the free surface are computed, by reducing the value of the parameter FREE SURFACE GRADIENT COMPATIBILITY from the default 1 to something between <0,1>, even downto zero (gradients computed totally piecewise).

In our examples we can try reduce the number and "steer" the place of occurance of the differences effectively only with this parameter. But because of the erratic character of these instabilities, some problems might still remain. This can be treated by changing the mesh structure locally, if you have an idea how the wetting/drying methods would work in these places.

Well, of course, this is a method from the shadowy backyard of the numerical methods, just a pain-easing tablet removing most of the symptoms, but not the cause of the disease. Sorry, the users of the parallel Telemac have to learn to live with it, this is typical for most ageing programs nowadays (and not only for programs, unfortunately...).

The other thinkable causes (and there quite a few possibilities in the very shallow shore areas) have been presently excluded.

Best regards,
jaj

Hello,

we have complaints from the users again, this time in another context. This time this is not changing the subdomains number, but working on assessing the water level changes due to shortening or lengthening of groynes training a river stretch. Comparing the effect of this measures (all runs with the same partitioning and without changing the horizontal mesh structure!) we have larger changes in the pattern of dried/wetted elements on river shores in some unexpected places, although the overall change in the water level due to this geometrical change is very, very small if not negigible. This looks very similar to the problem mentioned before, with the wavy instabilities changing their patterns, this time due to small geometry changes.

We will have runs now with increased solver accuracy (presently only 1.0E-6), changed wetting/drying threshold and, of course, playing with FREE SURFACE GRADIENT COMPATIBILITY (present value is 0.8).

Please inform me what would be your suggestions of getting rid of this instabilities.

Best regards,
jaj

Hello Jacek,

According to tests with automatic differentiation, elements with obtuse angles are a source of such differences, probably due to the fact that diffusion matrices on such elements give a negative diffusion. Anyway the horribly non linear behaviour of friction terms close to dry zones are certainly guilty also and this is still an open question.

Another thing: in your message I do not understand what is the wetting/drying threshold...

Last thing: we can discuss all this next week in your premises...

With best regards,

Jean-Michel

Hello JMH,

hmmmmm... I mean HMIN... I must admit I am a bit outdated in terms of Telemac, but how HMIN is set now? Via all that positive depths? Can't we influence wet/dry threshold anymore? Isn't any kind of clipping taking place anymore?

Yes, I also suspected some drastic switching on/off of friction term values when the depth is getting very small, exactly -- this is a very common disease in many codes -- is there an interacting threshold as well?

Our meshes are very nice, thanks to all that UnTRIM or DFlow FM orthogonality requirements taken into account in algorithms of Janet, our dearest mesh generator produces high quality meshes for Telemac as well.

Best regards,
jaj

Hello Jacek,

This HMIN should not have any influence, it is used only if you activate H CLIPPING, which is not recommended as it is not mass conservative.

JMH