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Hi,

I am using Telemac 2D to simulate a steady state open channel flow but am starting to question the suitability of the shallow water equations to do this given the geometry of the problem:

The channel is 1.37m wide and 17m long. At the inlet a discharge boundary condition is set with Q=0.1m3/s. At the outlet a depth boundary condition is set, with depth=0.3125m. These values are based on experimental measurements. Some literature states that the shallow water equations are only suitable when the depth is at most one tenth of the width of the domain it occupies (which is not the case for my geometry), so that vertical velocities are negligible in comparison with streamwise and tansverse velocities, so that hydrostatic pressure can be assumed. So my first question is as follows; is Telemac 2d suitable for simulating this problem?

After running the simulation, I get results that agree very well with experimental measurements (based on centreline depth along the channel) when using mesh edge lengths of 0.2m, 0.15m and 0.1m which suggested to me that I had achieved grid independence. However if the mesh edge length is reduced further (to increase mesh resolution), the steady state solution changes so that the inlet depth increases with increased mesh resolution. Is this happening because the shallow water equations are in fact not suitable for this problem because of its geometry? If so is there anything I can change in terms of solver settings or other that will allow me to still use Telemac 2D for this simulation? I have attached my run files along with a plot of centerline depth for different mesh resolutions in comparison with the experimental data.

Cheers

Danny

Hello,

I would say that shallow water equations can work in this case. When you do a sensitivity analysis of the mesh size you must change the time step accordingly, so that the CFL number remains the same, otherwise the numerical scheme will have a different behaviour. In your case the CFL becomes too large.

With best regards,

Jean-Michel Hervouet

Thanks Jean-Michel,

That seems to have solved the problem, I have just re-run the simulation with a smaller time step and results agree well with the previous courser meshes.

Cheers

Danny