open TELEMAC-MASCARET The mathematically superior suite of solvers

Hello,

I ran a test to see which numerical advection scheme was the least diffusive. Mostly to justify my choice with a quantifiable reason. I calibrated advection schemes (Leo Postma, N, PSI, LIPS) using my bulk roughness coefficient and kept all other parameters the same. Any differences can therefore be put down to numerical diffusion. I expected more diffusive schemes to calibrate at a lower roughness coefficient, however they all calibrated with the same value!

I know some of the schemes are more diffusive from the literature: the rotating cone test showed the N scheme was more diffusive than classical PSI, and the predictor-corrector schemes were less diffusive than either N or classical PSI. I can't think why they all calibrated at the same coefficient. Is there something in the theory I'm missing?

I've attached my *.cas file if it helps.

Many thanks!

Hi,

it is hard to answer without knowing your test case. I assume you simulate a more or less 1d steady state case?

For simple cases (1D channel, Manning friction) no model should fail, but when you start with a more variable topography there should be some differences. A good starting point are the 1d Mac Donald’s type solutions discussed in SWASHES (www.idpoisson.fr/swashes/).

Best regards,

Leo

Hi,

Thankyou for replying!

My channel is a single meander with topographic variation in x,y and z. I run the case until steady state is reached and the solution has converged. I use a base friction using Nikuradse with ks 0.01. I'm also using a bulk roughness coefficient CD to determine roughness values at the first four layers of the mesh (physically, this represents the projected area of the roughness elements.) I calibrated by altering the CD.

I've attached an example of my mesh representing the topography at part of the channel to give an idea.

The predictor-corrector schemes (LIPS etc.) used are based on the PSI scheme, itself based on a limited N scheme. I wonder if this similarity is the reason why? I have shallow zones but currently no dry zones. Without dry zones for LIPS to run implicitly on perhaps LIPS perform similarly to PSI?

Kind regards,

Hi,

ah, you already have a complex/real world problem. I don't know the differences of the Telemac 3D schemes and their implementation in detail.

I would check if there are really no differences in the velocity profiles (velocity over depth) and the resulting free surface?

Best regards,

Leo

Hello,

You're right the distributive schemes are all based on the N scheme. The PSI scheme is a limited N scheme and both have their predicotr-corrector variants.
To use them you choose the SCHEME OPTION FOR ADVECTION OF VELOCITY to 2 or 3 (for the 1st order and 2nd order predictor-corrector schemes). Option 4 is for tidal flats, it is an implicit version. These schemes are actually not called LIPS, which is a slightly different scheme only implemented in TELEMAC-2D. What do you mean when you say the calibration gives the same Nikuradse coefficient (which is actually the bottom roughness, which you can estimate from the diameter of the sediment grains)? How did you do the calibration?

Best regards,
Agnès

Hello

Thankyou for the information!

For the tidal flats predictor-corrector schemes (option 4) is it locally implicit i.e. implicit on tidal flats/ shallow areas and explicit elsewhere? Or is it implicit throughout?

Apologies, I should have clarified: I calibrated using the drag coefficient CD. I parameterised the drag as (in fortran):

where AREAU & AREAV is the projected area and AREAW the surface area of my roughness elements at the bed, and NORM is the velocity magnitude.

I calibrated by altering the CD value until the free surface slope matched that of my measured data. When testing advection schemes, by keeping all other parameters the same for each scheme and only adjusting the CD any differences between calibrated values could be said to be a result of numerical diffusion. However all the calibrated values were the same. There were some small differences however, for examples when testing sloped differences using RMSE method.

Kind regards.

Hi,

Sorry I don't really understand what you do: you're adding implicit source terms on all 3D points of the domain? To calibrate the model using the Nikuradse law I would just have started from an estimated value of the roughness and test slightly different values until I find the optimum. Same for Chezy or Manning but with estimated friction coefficients. Anyway, I don't think that the water level itself is affected by the numerical diffusion too much in a case like yours. You would probably see differences when comparing velocity values at some points of the domain for example.

I'm sorry I mistook LIPS and ERIA in my previous post. ERIA is only in TELEMAC-2D and LIPS is the option 4 for distributive schemes in TELEMAC-3D. LIPS is locally implicit for tidal flats. Without tidal flats, you should recover the same results as with the first-order predictor-corrector (option 2).

Cheers,
Agnès

I'm estimating the bed roughness by applying to four different layers at the bottom, essentially creating a "new bed" based on the spatial averages of bed elments taken from site measurements. To do this I'm adding head losses at the points that correspond to these layers. I haven't seen many differences in the way of velocity so far, however this may be due to the monitoring points I've selected.

Thanks for clarifying on the LIPS!

Kind regards.