Digital-Filter Based Synthetic Turbulence Generation Method for LES/DES Inflow
Velocity boundary condition generating synthetic turbulence-alike time-series for LES and DES turbulent flow computations. To this end, two synthetic turbulence generators can be chosen: - Digital-filter method-based 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):652-665. doi:10.1016/S0021-9991(03)00090-1 \endverbatim - Forward-stepwise method-based generator (FSM) \verbatim Xie, Z.-T., and Castro, I. Efficient generation of inflow conditions for large eddy simulation of street-scale flows, Flow, Turbulence and Combustion (2008) 81(3):449-470 doi:10.1007/s10494-008-9151-5 \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 length-scale sets) are fused into a new number set (stochastic time-series, 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 time-series 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 length-scale sets and small time-steps.
Resolved bugs (If applicable)
hierar.-parallel (1 2 2),
hierar.-parallel (1 2 4),
parallel-restart in terms of input Reynolds stress tensor components through
channel395DFSEM tutorial (one-cell 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:
- Spatial-variant Reynolds stress symmetric tensor (6-components)
- Spatial-variant mean velocity profile
- Spatial-invariant (for now) integral-length scale tensor (9-components)
The model output: Stochastic time-series involving the statistics of the model input sets.
The model computation has four subsequent steps:
- Generation of random-number sets obeying the standard normal probability distribution function
- Analytical computation of digital-filter coefficients as a function of integral-length scales in either Gaussian or exponential form
- Convolution summation between random-number sets and digital-filter coefficients
- Embedment of Reynolds stress tensor and mean velocity input into the digital-filtered random-number sets via elementwise multiplication and summation
Preliminary statistically-stationary results from a channel-height profile on the patch (one-cell domain
hierar.-parallel (1 2 4)):
Preliminary not-statistically developed (0.6 sec run, ongoing) with non-optimal input results from full
Preliminary comparisons with DFSEM suggests that the current model is ~1.8x faster for the
- Model is itself not divergence-free (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 interpolationis not fully functional.
- Code duplications with DFSEM exist for template funcs.
- For now, integral-length scale set (9-components) is spatial-invariant across patch.
- Further verification is ongoing through high-order statistics from Moser et al.'s DNS data, e.g. correlations, kinetic energy budget, enstrophy and so on.