open TELEMAC-MASCARET The mathematically superior suite of solvers

Dear,

I am modelling a horizontal flume in Telemac to check transcritical flow behavior.
I set up a test case with subcritical flow upstream and supercritical flow at the downstream boundary.
To do this, i used an upstream discharge boundary and a downstream elevation boundary.
My simulations reach a steady state and the boundary conditions were also respresented correctly.

However I was wondering how a model with supercritical flow at the downstream boundary can handle properly with a downstream boundary condition (prescribed elevation), since no information will be transferred upstream in the case of supercritical flow?

My guess is that TELEMAC finding out supercritical flow at the downstream section applies “free outflow” condition there?! Is this correct? And why is the elevation downstream then modelled correct to the prescribed value?

Thanks in advance!

In addition to my previous question I wanted to ask the folowing:

In modelling these discontinuous transcritical conditions (hydraulic jump, waterfall) and changing spatial resolution in the mean time, I was able to see that the codes spread the discontinuity over a number of space cells. I could see, that in decreasing space cell dimensions, this converges to real solution
How is this spreading exactly done?

Does the FEM induce spurious numerical diffusivity that increases with Courant Number or with the gradient of free surface?
Or is there a specific term of “artificial viscosity or diffusivity” added to the equations? Or is there an elimination of some terms from equations when Froude Number is near 1.0?

Thanks in advance

See relply to question on downstream boundary conditions.

I am surprised by the first question because, though there are a number of corrections done on boundary conditions, Telemac-2D does not do this one, for example when every thing at an exit is degree of freedom and the Froude number less than 1 we resort to 'incident wave' which is some sort of Riemann invariant theory). Not obeying a prescribed elevation would be too much for a user point of view so we do not correct this. So the prescribed elevation should be seen at the exit, and if not it is a mystery (Post Scriptum: actually Evert answered that yes he sees it).

On the second question, there is no specific treatment of hydraulic jumps nor changes of the algorithm depending on the Froude number, the fact that we find the correct jumps depends on the quality of the discretisation (as I wrote in my book, we do not even solve the conservative form of momentum equation). So this second question is a very good one. A beginning of answer is that linear finite elements cannot deal with discontinuities, and in cases with no discontinuity the conservative and the non conservative formulations are equivalent. The paradoxical question then is : when the mesh size tends to 0, do we converge towards the conservative (momentum conserved) or towards the non conservative solution (head conserved). The answer is : it is highly dependent on the discretization and the solution procedure. In the case of Telemac-2D we seem to tend to the conservative solution. The real limit has probably some wiggles or overshoots and is not so easy to find, it is certainly not a nice jump like an Heaviside function.

I hope this is useful,