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Hello everybody,
actually I'm working on a model of a small mountain torrent, during a flood event. In particular I'm investigating the effects of the water near some idraulic structures (bridges, weirs and an hydroelectric power plant) along the torrent during the transition of the flow peak.
Boundary conditions are steady, and do not change for the entire duration of the analysis.

Since high velocity are expected, and I also need a good mesh resolution (1 point every 10 cm), I've run the simulation with a small time step.
The simulation has gone enough to reach a permanent condition, and the results are good.

So, here's come some problems.

A time step equal to 0.01 sec gives me a scenario, while setting 0.02 sec I obtain a totally different result.
In both cases the courant number is low (no more than 0.5).

Has someone else faced this situation before?

Thanks a lot.
Riccardo

Hi Riccardo,
Yes I have found differences in results with time step for many applications even where courant number is not large, I generally found the results sensitive to the boundary conditions applied and to the solution scheme selected.

I would check your inflow rate throughout the computation (printed to the screen or to a file each listing step) to see if it achieves the same flow rate as specified by you, sometimes this can be different and often sensitive to the time step.

regards
Tony

Thanks for your feedback, Tony.
I always check the inflow and outflow rates, and they are really close to the imposed conditions.

In such situation I supposed that the smaller time step should be better...
In addition, with 0.01 sec the results show a smoother free surface, while with 0.02 sec there are more ripples.

Any others observations?

Hi Riccardo,

I've recently compared the HLLC scheme (finite volume scheme of TELEMAC-2D) with the so called scheme 14;5. During my studies I observed the same behavior for scheme 14;5. (no turbulence model, constant viscosity of 1.0E-6)

One may argue that the differences are often small, especially when the CFL number is smaller 1. However it is not pleasant. Especially since the HLLC scheme is less sensitive when the time step is reduced.


I'm not an real expert, but here are some hints which may help:

• You should check the Froude Number. Scheme 14;5 shows some oscillations when computing the wet dam break problem. I suppose that the scheme is maybe not stable for your flow situation.
• It sounds as if you look on "turbulent flow" (eddies) near structures. The flow (eddies) beneath a cylinder are very sensitive to the time step and are initialised by small numerical differences. So it is normal that the results can depend on the chosen time step.
• The simulation of boundary layers near structures can be very complex (see Finite Volume Methods for Hyperbolic Problems, LeVeque, 2002 for details). One has to consider the numerical viscosity of the scheme, the thickness of boundary layer, influence of viscous effects,...
• For complex problems with different cell size/speed the strong dependency on the time step could mean that one can not get a perfect CFL number for the whole domain.

Best regards,

Leo