open TELEMAC-MASCARET The mathematically superior suite of solvers

Hi everyone,

I have a general question about the diffusion of tracers:

The diffusion of a tracer, let's say in 2D horizontally, is determined by the HORIZONTAL DIFFUSION COEFFICIENT FOR TRACERS combined with the numerical diffusion of the solver? The numerical diffusion is dependant on the mesh resolution. The larger the mesh size the larger the numerical diffusion.
If this numerical diffusion is exceeding my physical diffusion of the tracer I want, the tracer will move trough my mesh too quickly, correct? The horizontal diffusion coefficient is of no importnace anymore at that point. Is there a way to counter the numerical diffusion in order to get a lower tracer diffusion in the model?

Does anybody have experience with the numerical diffusion of the different solvers? Which one has the lowest numerical diffusion? What are the best settings in 2D or 3D to minimize the numerical diffusion?

Sven

Hello Sven,

This is all correct. For tracers, if we want monotonicity and mass conservation, the only possibilities left are the distributive schemes in finite elements and nearly all the finite volumes, but the latter with smaller time steps that generate also a lot of numerical diffusion. If you add tidal flats only scheme 14 (NERD) will stay in finite elements.

If you have no tidal flats, look at the new options for distributive schemes in version 7.0 (SCHEME OPTION FOR ADVECTION OF TRACERS 2 and 3), they are much less diffusive for unsteady states.

In the next version we have a new implicit distributive scheme which has much less diffusion both for unsteady and steady situations, due to 2 different important improvements, this will be presented in the next TUC and is already in the trunk.

What show our tests is that the mesh is also very important, possibly much more than the order of the scheme, the best being to have a mesh aligned (as far as possible...) with the streamlines.

With best regards,

Jean-Michel Hervouet

Jean-Michel,

I want to implement a space varying horizontal tracer diffusion coefficient. I would create a map in blue kenue, like with BOTTOM or BOTTOM FRICTION and read this at start of simulation. (I already made this work for initial salinity field). I know how to do this, but I have no idea yet how difficult it would be the replace the parametervalue of the diffusion coefficient with a vector (containing a different value for each node of the mesh)
Since you know the code better, do you think I can do this without too much changes in the code? Which subroutine handles the tracers?

Sven

Hello Sven,

I suggest that you choose turbulence model 1 (constant viscosity) and modify subroutine VISCOS, where instead of giving the same coefficient, as you will see, you can give every node a specific value. You can do this only for tracers if you want, then see the loops from 1 to NTRAC.

Regards,

Jean-Michel

Last question:

can I give negative diffusivity values? Physiccally this is possible that some chemicals move against the concentration gradient. This is called uphill diffusion. I tried to give a negative value, but it doesn't seem to have an effect?
The idea was to use uphill diffusion to tackle a bit the numerical diffusion in areas where it is too big.

Sven

Hello,

Negative diffusion can be unpredictable and lead to infinite values, so I would be somewhat reluctant to do that. Another problem is that numerical diffusion is a real diffusion only in very simple cases, like upwind advection in 1D with constant velocity and regular gridding, so antidiffusion will not exactly cancel it in more complicated cases.

With best regards,

Jean-Michel