open TELEMAC-MASCARET The mathematically superior suite of solvers

Hello,

While trying to ensure I fully know what I am doing, I juxtaposed the telemac2d manual with "Hydrodynamics of Free Surface Flows", Jean-Michel Hervouet, Wiley. May I please ask for clarification on a few description in the manual.

First, we have been using the (default) numerical scheme combination, 1;5;1;1. According to the manual "The default value is 1;5;1;1, which corresponds to the use of the method of characteristics in all cases, except for depth for which the appropriate conservative scheme is selected by the code. Note that the value 5 in second position does not mean `psi distributive scheme` but is the value used by the previous version of TELEMAC-2D to select the conservative scheme for depth." May I enquire if the value 5 indeed picks the mass-conservative Positive Stream-wise Invariant distributive scheme? Please excuse my paranoia on this one.

Second, the manual clearly states the default value of the number of non-linear sub-iterations, but may I enquire what the precise defaults for the relaxation coefficients are? The book suggests 0.55 or 0.6 .

Third, the manual points out that the IMPLICITATION FOR ... keywords control the inplicitation parameters, but goes on to state "The default values are generally adequate". May I enquire what the exact default values are? The book here suggests a value greater than 0.5, but close to 0.5

Many thanks for your time and help.

Best!

Alexandros

Hi Alexandros,

you can find the default values for all parameters in the .dico files in your sources folder. E.g. for Telemac2D in ...\v7p1r0\sources\telemac2d\telemac2d.dico

There are all keywords with their parameters and defaults listed - often it is better to check there

Hope this helps,
Gabi

That is fantastic, Thank you.

Hello Alexandros,

Some explanations further to what you can see in the dictionary of keywords:

the number 5 in the list 1;5;1;1 is really obsolete, it refers to a time when some schemes were not mass conservative for water, we have now removed them all, and there is nothing left to choose regarding advection of depth (this "advection" of depth stemmed from splitting div(hu) into h div(u) + u.grad(h), this latter term being like an advection).

Non-linear sub-iterations are only useful for rather short waves, it is virtually useless if you are not playing with solitary waves or flows that are actually not in the validity range of Saint-Venant equations.

For the implicitation coefficients I would say it is about the same, for quasi steady flows in rivers you can have them equal to 1, it stabilises the computation. It may however be a bit smoothing for tidal waves.

With best regards,

Jean-Michel Hervouet

Hello and thank you for your response.

What drives my questions is understanding exactly what discretisations are used for each equation in the Saint-Venant equations, as we are also trying to perform model inter-comparisons. Any pointers in that direction will be greatly appreciated.

Hello, I have just gotten round to looking into all the information again and some details are now settled, but other questions have popped-up.

Having looked into the book & manual again it is therein made clear that the method of characteristics is used for all variables, in the first stage of the fractional step method. The question then becomes is the weak formulation of the method of characteristics used when we choose to solve the Saint-Venant with FE?

Second I followed @gh_river 's pointer and found out about the implicitness of both the propagation and diffusion terms ( in the second stage of the fractional step method). For the sake of completeness may I please enquire about the implicitness of bottom friction, "vertical-structures-friction", buoyancy and Coriolis terms? In fact dragfo.f in various examples suggests that "vertical-structures-friction" terms are fully implicit. Also sources/telemac2d/prosou.f suggests bottom friction to be semi-implicit, but no implicitness factor is given. I had little luck finding about the Coriolis term implicitness (using, I must admit, just grep in the telemac2d directory).

Thank you a priori for your time and help.

Hello,

Yes, the method of characteristics is the default for historical reasons but though it works well for velocities, it is not recommended for tracers as it is not mass conservative. The strong form is used. The weak form of characteristics is slightly not mass conservative and not monotone, so it is not recommended, even if it works very well in the case of the rotating cone and of the flow around bridge piers, because of its very low numerical diffusion, which gives e.g. an excellent behaviour of von Karman eddies.

On the implicitation of friction or drag forces, we want to avoid that the friction terms give a backwards velocity if the time step is too large, so the only possibility is that the terms are formally fully implicit. However these terms are proportionnal to the square of the velocity, so we take one velocity explicit and the other implicit, so it is also a semi-implicitation even if it is not like a Crank-Nicholson scheme. Doing this there is no choice of implicitation coefficient, we make the decision for the user.

With best regards,

Jean-Michel Hervouet

Thank you, for a thorough and authoritative answer!