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Bonjour à tous,

I would like to model a regulated reservoir as shown on Q3.jpg where upstream boundary is the most at North. At this location, I have inflow data.




At downstream location, (see Q2.jpg) the computational domain is cut just before power canal since i do not have precise bathymetric data. Turbined flows and water height are available at this point.





I seem to understand that using downstream prescribed flowrate is not 'good practice'. However, when I use historical water height as prescribed elevation at downstream, I never get close to historical turbined flow since water inflow takes quite a while to reach the dam. Ideally, i would I have used prescribed flowrate at both up and downstream and try to calibrate friction to get close to historical water height. Furthermore, the reservoir has relatively big water stock capacity so it takes about a day for turbined flow to have significant influence on the water depth.

To summarize, my questions would be :

1. In that case, is it OK to use prescribed flowrate at both end of the reservoir if numerical convergence happens??? If not, how would you model the outflow of my problem ?

2. Does somebody knows a piece of literature that explains in details why using prescribed flowrate at downstream is not ideal?


Merci beaucoup pour votre temps


Mathieu

Q-Q boundary is posible although not advised. I recomend you try. All you need is a good stretch of slope over which natural flow can be established.

If you have a problem with unstabilities on the downstream, maybe you can try using sinks instead of an open boundary but keep an open boundary if you can.

Hope this helps,
Sébastien

Hi Sébastien

Thanks for reply

I tried Q-Q boundary. During computation listing, I can see that flow exiting the domain (158 m³/s) is close but not exactly what I prescribed (150 m³/s). I have keyword CONTINUITY CORRECTION activated since I get a volume lost too high if it's deactivated at end of computation. The whole computation seems to converge with around 10 iterations for each time step no matter if CONTINUITY CORRECTION is active or not.

Is that what you mean by downstream unstabilities ?


I will try with sinks and compare the results.

In the meantime, do you know a CFD book (perhaps M. Hervouet's book ???) that explains the basic theory of why

Q-H boundary > Q-Q boundary > Q-"sinks" boundary



Mathieu

Hi Mathieu,

In theory, you can use any kind of boundary conditions (elevation, flowrate) at the inlet or at the outlet.
The theory of hyperbolic PDE tells us that, the regime (subcritical or supercritical) who manages the need of a boundary condition.
For a subcritical regime, only 1 condition is necessary for inlet and 1 condition for outlet
For supercritical case, 2 conditions are necessary for inlet and 0 condition for outlet.
Numerically, with Finite elements, we impose weakly (on h and u) the boundary condition in all cases. The code will take into account these conditions in the way who satisfies the variational formulation (weakly), in opposition to the strong imposition which causes some troubles with stability.
Moreover, the imposition of a flowrate, means the splitting the outflow and its sharing between all the liquid boundary nodes without any disctinction; which is not optimal especially if you have a compound river channel.
Henceforth, if we combine the numerical and the theoritical constraints, you can see that it is necessary to keep on eye the flow regime and to impose preferably an elevation (more efficient numerically) than a flowrate at the outlet of the model.

You can find much more details in the Hervouet's book.

With my best regards.

Riadh ATA