open TELEMAC-MASCARET The mathematically superior suite of solvers

Hello,
I read on this forum that the artificial diffusion of an upwind advection scheme is about U*dX/2 where U is the velocity and dX is the mesh size.
In the manual of TELEMAC I saw that I can adapt the type of advection. In my model I use the default value (the method of characteristics). Is the artificial diffusion of this method is U*dX/2?

Could you please tell me what is the most stable scheme with the smallest artificial diffusion?

Thank you in advance.
Tatiana

Hello,

The answer depends on the Courant number... The method of characteristics (1) is better than other schemes with high Courant numbers (but it is not conservative, so use it preferably for velocities, not for tracers). Otherwise SUPG is the next, but will properly work only for Courant numbers between 0 and 1, it gives non symmetric linear systems. After, the best is the distributive PSI scheme 5 (with an adaptive sub-stepping for stability). However scheme 4 (N scheme) is never very far from PSI scheme. With tidal flats only characteristics and N distributive schemes in adapted form (14) will work.

I hope this helps, regards,

Jean-Michel Hervouet

Thank you very much for your answer. I’ll use the method of characteristics for velocities. Is the artificial diffusion of this method U*dX/2?

Best regards,
Tatiana

Hello,

Not exactly, it is more complicated, depending on where the foot of a characteristics is, in 1D the method of characteristics is exact for integer Courant numbers. However basically it is first order in space and time.

Regards,

JMH

Ok, thank you.
I’m modelling the flow velocities in the port of Terneuzen in the Western Scheldt. The entrance of the port is about 320 m wide. The grid size is 10 m in the study area and the time step is 3 seconds. The Courant numbers are higher than 1 but smaller than 10.
I attached the selafin file and steering file. I use the default turbulence model and the default type of advection.
I don’t want to have too high artificial diffusion in the model. Could you please tell me if I’m using appropriate parameters for this modelling case? Or should I use different type of advection and adapt my time step?

Best regards,
Tatiana

The attachments are here.

Hello,

It will be easier to tune your model in view of the first results, the number of iterations of solvers, etc., the only thing I can say is that in your case (TREATMENT OF THE> LINEAR SYSTEM = 2) the GMRES solver (SOLVER=7) is not useful. Put conjugate gradient (1) instead, it will certainly be faster. Another thing is that you do not give any diffusion, so it will be 1.E-6 m2/s ?

With best regards,

Jean-Michel Hervouet

Hello,
Thank you very much for your answers. I'll try different parameters and I'll check my results.

Best regards,
Tatiana