Telemac-AD Adjoint Example 4: Piers and Eddies

More detailed Description: Telemac Users Club 2016:

A group of bridge piers in the Danube producing vortexes, calculated with Telemac 3D.




Vertexes / Eddies / Flow fields induced by obstacles  (e.g. salinity or temperature):

  • How does the shape (x,y,z coordinates) affect the field of flow, here: development of Karman Vortex Streets?


Inverse Problem: As potentially any points bathymetry value X, Y, Z in the model affects the vorticity indicator.

Experimental Setup:

Upper Picture: Estimating vortex zones with the “weak form of characteristics” option produces results that comply with Kármán’s formula for the vortex creation frequency. Lower picture: The time averaged vortex corridor.

This is an academic example to show the usage of adjoints for shape optimization.

Interpretation of the resulting adjoints as a map:

The pictures show a wake behind circular pier. From empiric formulas we know the vortex creation frequency and the point of creation (here ~80° left and right against the upstream face center) Additionally, several flume experiments are available for comparison.

Especially the boundary points on the downstream side of the pier have a strong impact on the vorticity. Inner points only have limited effect which comes from the vertical component (Z coordinate) and the boundary roughness.

The alternative picture shows the three adjoints for x, y, z coordinates as gradient arrows in the direction which would reduce the asymmetry.

Download and experiment with the show case:

The example is available for Download as ZIP: -> Link (Registered Users Only!)
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The magnitude of point coordinate adjoints clearly shows the dependency of the vorticity to non-boundary points. This means that shifting one of the coloured points in 2D will lead to slightly other results inside of the selected zone (orange polygon). Due to the logarithmic scale, the pink coloured boundary points have a 100 times stronger impact than the blue coloured surroundings. However, the blue area is up to 100 times larger.


The executable is compiled for Linux 64bit.

  • Unpack the folder
  • Open a teminal in this folder and execute „./pier.exe“
  • Results will appear in the file „T2DRES“ in the same folder





If the adjoints are displayed as arrows, they show the direction a mesh point has to be moved to increase the vorticity inside the pink selected area. The opposite direction would reduce it. In particular, the direct boundary points give the expected answer: Shift them to the inner side, and the vorticity will be reduced.