turbulentDFSEMInlet: potential issues
 The results presented in the journal paper for the Reynolds stress tensor of Moser et al.'s (1999) smoothwall plane channel flow with
Re_\tau = 395
(Fig. 4) could not be reproduced with or without CFD despite all our efforts. (We are more than happy to be proven incorrect in our attempts.) In the release notes of v1606+ (link), a high level of resemblance to the journal paper results as well as the benchmark results were reported.
 These results were unfortunately revealed to be involving a case setup error: the integrallength scale input was incorrect in those tests; more specifically, they were almost zero.
 I think the reason why we had obtained fairly good results in the release notes is due to the
nCellPerEddy
term (which doesn't exist in the original journal paper)  that dominated the integrallength scale computation for relatively lowvalued integrallength scale input sets.
 Similar observations had been made by various CFD developers/users as well. For example, Kopper (2017) has stated in Implementation and Verification of a Synthetic Eddy Method (SEM) in the Eagle3d Compressible Flow Solver (SEM) in the Eagle3d Compressible Flow Solver for failed attempts of a DFSEM implementation into the solver
Eagle3D
:
 In the release notes of v1606+ (link), a high level of resemblance to the journal paper results as well as the benchmark results were reported.
While his published results are impressive and OpenFOAM Ltd announced the implementation of this method in the current OpenFOAMplus release (OpenCFD Ltd, 2016), Poletto’s results could not be reproduced using the currently available versions of OpenFOAMplus and CodeSaturne.

See the following OpenFOAM results obtained from a replication of the journalpaper test case using the DNS dataset provided by Moser et al. (1999) / /data/MKM/chan395 (i.e.
verificationAndValidation/turbulentInflow/oneCellThickPlaneChannel
) (and compare it with the original Fig. 4). The input wallnormal profile of integrallength scales were computed by using the xcorrelations (correlations) as well as k^1.5/epsilon (balances) provided by the DNS dataset (both approaches resulted similar scale values). The input Reynoldsstress tensor was obtained from chan395.reystress. The Reynoldsstress tensor results were sampled on the patch of the computational domain. Sampling has been performed with different sampling methods available in OpenFOAM to avoid any potential pitfalls existing in one of the sampling methods. Also note that the patch and entire computational domain were preserved in a single processor to prevent any parallelisation effects. 
Reynolds stress tensor results sampled on the patch:
 Reynolds stress tensor results sampled on the firstinlet cell centres:
 Mean streamwise velocity component sampled on the patch:

Using the complete channel case also could not help to reproduce the Reynolds stress tensor results of the journal paper (Eqs. 1315). See the test case and results in !454 (merged).

One of the potential culprits we have identified is the coefficient
C1
in Eq. 11 being used in Eq. 10, which is at the heart of the DFSEM.
C1
in Eq. 11 has units of m^(1/2), yet it must be dimensionless for Eqs. 910 to be dimensionally consistent. Checked also the thesis, whereat
C1
expression is identical to that in the journal paper.
 Checked also the thesis, whereat
 This sounds a minor issue (which should easily have been picked by the reviewers of the journal paper, I believe), but Eq. 11's
Vo
term affects the instantaneous velocity field as well as the Reynolds stress tensor  refer to #1744 and #1004.  Changing the
sqrt
tocbrt
, like suggested by Michael, can alleviate velocityfield issues, but some local tests indicated that the change could cause scaling issues for the Reynolds stress tensor this time.  No explanation was given on how
C1
was derived.


Another culprit might be the
C2
in Eq. 12 which should also be dimensionless. No detailed derivation or elaboration was given onC2
in the journal paper or in the thesis; hampering the reverse engineering. 
One problem is related to the average length scale expressed in Eq. 14. Assuming
\Delta {x,y,z}
are the local mesh size, this equation returns the local mesh size as the average length scale of the flow for any input length scales larger than the local mesh size. For example,L=0.1
,\kappa \delta = 0.41
, and\Delta {x,y,z} = 0.01
 this expression returns the length scale as\sigma=0.01
rather than the input L. 
Another problem we observed in the DFSEM is that the reproduction of input Reynolds stress tensors on a patch is severely affected by input choices for integrallength scales without any deterministic relation between the two.

Also, we have observed that, due to the (theoretical) limiters being applied on input integrallength scales, the scales generated on a patch differ from the user input. For example, if the user measures autocorrelation function on the patch with Taylor's hypothesis and calculates scales from the autocorrelation, the (physical) input scales and calculated scales will likely be different. For this reason, this situation leaves us with a method which could not reproduce user inputs of the Reynolds stress tensor and integral length scales on a given computational domain patch (i.e. no CFD effects) and inside the domain.

DFSEM method does not allow any input length scales larger than
kappa*delta
wherekappa
is the von Karman constant anddelta
is the characteristic length of the domain. The rationale of this is the premise that a length scale of an eddy cannot be larger than the domain length. However, this premise is only valid for lateral directions in a wallbounded flow and is not valid for freestream flows. In a wallbounded flow, the streamwisedirection components can be larger than
kappa*delta
. This was even showed in one of the figures in the original work  the linearlyincreasing line is computed from Moser et al.'s (1999) DNS computation:
 However, this premise is only valid for lateral directions in a wallbounded flow and is not valid for freestream flows. In a wallbounded flow, the streamwisedirection components can be larger than

The method is reportedly divergencefree. However, to what extent the solenoidal field persists inside a CFD domain is unquantified. Also, it is not clear whether the pressure fluctuations were reduced due to the divergencefreeness of the method or the adhoc application of the mass flux correction.

Various solution suggestions:
 Discard DFSEM, or limit its usage for isotropic turbulence cases.
 Replace DFSEM with the other SEM variants being developed by Uni. of Manchester, since to our observation, the active developments and usage on DFSEM in the originator institute has been ceased as well in favour of other SEM variants being developed thereat.