Our paper on Synthetic turbulence generation with PyFR has been recently published in the AIAA Journal, see here. The paper describes in details the extended Synthetic Eddy Method that was introduced previously in one of our seminars here, where you can find also some additional results.

The main features of the method are the following:

- source term formulation, which allows synthetic turbulence to be injected anywhere in the domain
- full anisotropy of the length scales (with a limitation on the minimum length scale ratio for a given direction, see eq.(16) in the paper or slide 13 of the seminar)
- works with the compressible and with the incompressible solver

The main limitations, which can be lifted with a bit of development, are the following:

- homogeneous turbulence in the z direction, which is assumed to be the spanwise direction
- the x-direction is assumed to be the streamwise direction

In the electronic supplemental material associated to the paper one can find the source files, mesh files and input files.

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A more recent version of the source can be obtained by checking out this github branch. In particular, this has been updated up to v1.12.2. Regarding the turbulence generator, there are a few implementation details that have been changed compared to the version published with the paper. For instance, the eddies’ data is stored directly in the solution file, rather than in a separate .csv files. Also, the turbulence generator loops over only the 5 eddies closest to a given element (rather than looping over all eddies), which are determined using a kd-tree. A consequence of this latter implementation strategy is that the overhead of the turbulence generator is almost independent of the total number of eddies (at least for N <150) and also that the custom load-balancing strategy might not be necessary anymore. Preliminary tests gave a slowdown of less than 10% with standard mesh partitioning.

Here is an example of the relevant section that should be in the .ini file:

```
[soln-plugin-turbulencegenerator]
; how often to update the location of eddies
nsteps = 1
; reynolds stress components. can be function of xyz
r00 = 0.2
r11 = 0.05
r22 = 0.1
r01 = 0.001
; length scales, can be function of xyz
l00 = 0.3
l01 = 0.2
l02 = 0.2
l10 = 0.2
l11 = 0.1
l12 = 0.1
l20 = 0.1
l21 = 0.1
l22 = 0.1
; reference lengths, see eq. (14) in the paper
lturbref = [0.3 0.2, 0.1]
; Bulk velocity
Ubulk = 1.0
; bulk velocity direction 0=x, 1=y, 2=z. (x recommended)
Ubulk-dir = 0
; center of the turbulence generating plane
center = [-1.0, 0.0, 0.1]
; dimensions of the turbulence generation plane.
; if x is streamwise, these two represent the dimension of the plane in y and z
plane-dimensions = [1.0, 0.2]
; mean density and mean mach number. Only needed for a compressible solver.
rhomean = rho0
Mmean = Ma
```

Finally, for those interested in profiling and optimisation, with the help of @WillT I have created a standalone version of the relevant kernel, see this file and this file.

They can be compiled with:

`nvcc -pg -lineinfo -O3 --gpu-code=compute_70 --gpu-architecture=compute_70 --std=c++17 --use_fast_math --fassociative-math single.cu negdivconf.cu -o go`

and profiled with nvidia nsight.

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