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Hello,

we have a case in which we try to model a confluence of two rivers, one of which carrying a lot of bed load to another, so that a kind of sand bank at the confluence builds up, which is crossed by the current with ever smaller depth leading finally to drying-out on the top of the growing sill. Also a variant is being computed, in which the sand bank is stabilized -- so with areas with non-erodable bed.

We observe awkward oscillations of the free surface (and the bottom as well?) around the sill. On some single "dried out" nodes the bottom level grows although the nodes have no velocity.

The question is if Sisyphe/Telemac-2D can manage this kind of strongly coupled and non-linear situation, and even worse, with drying-out. Please note that the flow over the sill/bank changes in Froude-Nr. from 0.3 to 1.5 and back to 0.5, deep-shallow-deep transition, however with a general current direction along the bank.

Best regards,
jaj

Hello jaj,

maybe the the oscillations come from the Telemac-2D?
Our experience is that the combination of transcritical flow & longer-term coupled sediment transport simulations can be fatal since small oscillations can build up with mutual feedbacks between the two modules. Sometimes it is really hard to get a stable and convergent simulation when using the FE solvers for such cases.
So you could try to use in Telemac-2D the Finite Volume HLLC solver and see what happens. We use it for dam-break type problems with transcritical flow, Froude numbers going up to 10, a lot of wetting and drying and it works well in combination with Sisyphe. However it doesn't account for turbulent diffusion which in advection dominated flows doesn't play a large role and the rest gives you the numerical diffusion . And you need some more computer power.

Hope this helps,
Clemens

Dear Konsonaut,

I am not resposible for the before mentioned model, but asked for an opinion as so-called "expert" (I have programmed in Telemac-3d years, years ago...). But I try to explain as much as I can.

(1) Yes, the oscillations come up definitely "from Telemac-2D" or speaking exactly: wave-equation algorithm, with edge-based N-scheme (14) for velocity and cons. PSI-scheme for depth (5) advection, but with a huge momentum dispersion on (Elder!) and therefore relatively small "physical" roughness. The user applies only very small damping of the "natural" P1P1-element-oscillations. So my advice here was to apply characteristics and stronger damping first.

(2) Second, the occuring sand bank is rather badly resolved, because it just occurs and grows and then appears as a flow obstacle, along three nodes we have a transition sub/super/subcritical flow...). So, the place in question must be better resolved and the time step must go down (although the characteristics could help with larger Courant numbers).

(3) Of course the results must be reached with impoved numerics first, however I have my headaches if the areas drying-out due to the deposition of material brought by the bed load only (no suspension!) can be modelled properly, imagine a shoreline moving -against- the current and transport direction. This is not what the traditional Exner equation has been set for.

(4) The idea with the HLLC solver is good, but remember we have two typical lowland rivers with only a locally occuring transcritical flow -- just over the appearing sand/gravel bank -- so I would really prefer to use only an advection scheme which is proven to deal with the situation appropriately, than to switch to hyperbolic module completely for the whole model. Would the bed load be coupled with the SWE-hydrodynamics directly, I would immediately recommend it. The INTERaction between bed load and transport is in this case probably too massive to justify a decoupled model usage, which is governed by the flow and strongly assuming very small morphodynamical changes pro time step (like Sisyphe).

Anyway, thank you for your comment. What are your experiences with this HLLC solver and some non-erodable beds or obstacles? Drying due to the bed load brought and deposited, and not due to water-level changes?

Best regards,
jaj

Hello,

Yes, the P1P1-element-oscillations can be very very annoying. Doing only hydrodynamic calculations one may overlook them but in longer-term sediment transport simulations the effect influences significantly the calculated bed levels <-> water surface elevations with the simulation time.

To dig out an old post related to this where we had and still have no satisfying solution:
www.opentelemac.org/index.php/kunena/17-...n-the-evolution#5140

To 2 and 3: Yes, better resolving such an area would help, or/and maybe switch to Telemac-3D if the underlying processes are outside of 2D depth-averaged assumptions?

I personally don't think that the direct coupling would resolve your problems. Tests from the ETH Zürich colleagues showed that even in dam-break type simulations with huge erosion and deposition processes within one time step, the direct coupling gives almost no difference to the decoupled approach.

"Drying due to the bed load brought and deposited, and not due to water-level changes":

The HLLC solver works well because it can handle such situations like lake at rest, drying of a beach, which are some of the typical validation cases for FV schemes. Maybe such challenges correspond more or less to your problem. Do the FE schemes in Telemac-2D have the same good properties in such cases? I would be interested to know it since I'm not an expert in numerics.

Best regards,
Clemens

Dear Konsonaut,

yes, ignoring Telemac-2D instabilities in long term simulations is deadly. It is extremely naive not to supress them if you try to deal with any transport phenomena. Therefore I recommended to get rid of instabilities first.

Telemac-3D would be an answer maybe, at least for steep slopes, but I am not sure if helpful when drying and wetting occurs. The drying/wetting treatment in both T2D and T3D ary pretty the same (local manipulations) with the complication of sigma mesh levels coalescing: meeting in one point...

Please note most (or at least all I know) models with direct bed load and current coupling are hyperbolic Godunov/Riemann etc. where the time step must be so small, even by implicit treatment. Then you might not see difference uncoupled/coupled, because the morphodynamic is usually much slower... Anyway, a good question, not answered in the case of general flow models (which allow also flows which are not hyperbolic).

But please note that I am not mentioning drying and wetting due to changing waterlevels (i.e. as if there were no bed load) but due to depositing material brought via bed load (horizontally, with no suspension!) So I do not mean drying-out of a beach, because e.g. of a tide, but letting the beach occur due to the sand brought by the current and left there. And that's it.

Best regards,
jaj

Hello,

ok, what I intented by mentioning the cases like drying out of a beach or lake at rest was that your situation ..wetting drying due to bed load evolutions.. in the end can be seen as similar to these validation cases.

Enclosed you find a small video (maybe it is not allowed to upload) and a picture showing the longitudinal cut of an evolving dam breach. The material is transported downstream, it accumulates at the toe of the dam to a steady state and with accompanied drying processes where water is flowing to the left and right side or not. So I think this corresponds more or less to the topic which we are discussing about. In the end in the whole model we have some super stable small ponds and super steady state conditions. I like this.


Have a nice weekend,
Clemens

Dear Jaj,
I've little experience dealing with supercritical flows and sediment transport. But a couple of years ago I've worked with a student on the numerical simulation of bar formation and propagation under flows with Fr > 1.
I was surprised that without any modification of the numerical schemes or transport formula (we used MPM), the model was able to reproduce nicely the expected pattern.

Best wishes,

Pablo

Dear Clemens and Pablo (welcome),

your dam break example is much simpler than we have, at least in terms of mathematics. It is virtually 1D, whereby our case is definitely 2D!

Well I am not sure if I am allowed to publish any pictures here, therefore just a description:

Imagine the first (upper left corner) picture of your previous post represents a fragment of a cross-section of a river confluence, with your dam being our sand bank in the middle of the junction, which actually grows in the amplitude instead of diminishing. Both rivers, left (smaller) and right (larger) of the sand bank flow towards the picture viewer. The river to the left has a slightly higher water level than the one to the right, so that the current of the left river veers towards the right river, flowing over the top of the bank. Both rivers carry bed load, the left river more. The sand bank grows longitudinally (with the main current) as well as laterally and grows in the amplitude so far, that the flow overtopping get supercritical and then even drying-out of the sand bank occurs.

A variant is being computed as well in which this bank is stabilised by a longitudinal dam -- with the nodes in the middle of the bank being marked as non-erodible.

In both cases instabilities of the surface occur -- and it seems also of the function describing the bottom level. On the both sides, luv and lee. In the second case (non-erodible nodes) we have even an awkward situation in which the bottom levels of non-erodible nodes -- in terms of the hydrodynamics dried-out and with null velocity -- grow up into very high values, making the results inacceptable at all.

Any hints (apart from higher resolution, characteristics and free surface stabilisation?)

Best regards,
jaj

Hello,

a small addition, but an important note -- I've been just told the "overgrowing skywards" of the bottom line on seemingly dried-out nodes occurs also in erodable areas as well, so this awkward feature is not connected specifically with non-erodible areas.

Best regards,
jaj