DigitalFilter Based Synthetic Turbulence Generation Method for LES/DES Inflow
Summary
Velocity boundary condition generating synthetic turbulencealike
timeseries for LES and DES turbulent flow computations.
To this end, two synthetic turbulence generators can be chosen:
 Digitalfilter methodbased generator (DFM)
\verbatim
Klein, M., Sadiki, A., and Janicka, J.
A digital filter based generation of inflow data for spatially
developing direct numerical or large eddy simulations,
Journal of Computational Physics (2003) 186(2):652665.
doi:10.1016/S00219991(03)000901
\endverbatim
 Forwardstepwise methodbased generator (FSM)
\verbatim
Xie, Z.T., and Castro, I.
Efficient generation of inflow conditions for large eddy simulation of
streetscale flows, Flow, Turbulence and Combustion (2008) 81(3):449470
doi:10.1007/s1049400891515
\endverbatim
In DFM or FSM, a random number set (mostly white noise), and a group
of target statistics (mostly mean flow, Reynolds stress tensor profiles and
lengthscale sets) are fused into a new number set (stochastic timeseries,
yet consisting of the statistics) by a chain of mathematical operations
whose characteristics are designated by the target statistics, so that the
realised statistics of the new sets could match the target.
Random number sets >

DFM or FSM > New stochastic timeseries consisting
 turbulence statistics
Turbulence statistics >
The main difference between DFM and FSM is that the latter replaces the
streamwise convolution summation in DFM by a simpler and a quantitatively
justified equivalent procedure in order to reduce computational costs.
Accordingly, the latter potentially brings resource advantages for
computations involving relatively large lengthscale sets and small
timesteps.
Resolved bugs (If applicable)
Verified for serial
, scotchparallel (4)
, hierar.parallel (1 2 2)
, hierar.parallel (1 2 4)
, serialrestart
, and parallelrestart
in terms of input Reynolds stress tensor components through channel395DFSEM
tutorial (onecell domain).
Checked for various possible (commonly encountered) wrong inputs, e.g. arbitrary Reynolds stress tensor components.
Details of new models (If applicable)
The model input:
 Spatialvariant Reynolds stress symmetric tensor (6components)
 Spatialvariant mean velocity profile
 Spatialinvariant (for now) integrallength scale tensor (9components)
The model output: Stochastic timeseries involving the statistics of the model input sets.
The model computation has four subsequent steps:
 Generation of randomnumber sets obeying the standard normal probability distribution function
 Analytical computation of digitalfilter coefficients as a function of integrallength scales in either Gaussian or exponential form
 Convolution summation between randomnumber sets and digitalfilter coefficients
 Embedment of Reynolds stress tensor and mean velocity input into the digitalfiltered randomnumber sets via elementwise multiplication and summation
Fidelity:
Preliminary statisticallystationary results from a channelheight profile on the patch (onecell domain channel395DFSEM
case: hierar.parallel (1 2 4)
):
Preliminary notstatistically developed (0.6 sec run, ongoing) with nonoptimal input results from full channel395DFSEM
case:
Performance:
Preliminary comparisons with DFSEM suggests that the current model is ~1.8x faster for the channel395DFSEM
tutorial.
Risks
 Model is itself not divergencefree (yet convertible); therefore, should not be preferred for aeroacoustic applications as is. Nonetheless, the mass flow rate correction reduces the inlet pressure fluctuations to the level of Poletto et al.'s DFSEM (quantified and verified by Bercin in comparison to Moser et al'. DNS data for pressure fluctuations and correlations).
 For now, Taylor's frozen turbulence hypothesis is applied in the streamwise direction.
 For now,
bilinear interpolation
is not fully functional.  Code duplications with DFSEM exist for template funcs.
 For now, integrallength scale set (9components) is spatialinvariant across patch.
 Further verification is ongoing through highorder statistics from Moser et al.'s DNS data, e.g. correlations, kinetic energy budget, enstrophy and so on.