Unsteady Simulations for Industrial Flows:
5, 7, 9 December 2022
A three-day online course
Large Eddy Simulation (LES), hybrid LES-RANS, Detached Eddy Simulation (DES) and unsteady RANS.

LES is suitable for bluff-body flows or flows at low Reynolds numbers. To extend LES to cover industrial flows at high Reynolds numbers, new approaches (hybrid LES-RANS, DES, URANS, SAS, PANS, PITM) must be used. They are all based on a mix of LES and RANS. The course will give an introduction to LES and these new methods.
LES, or any of the new approaches, is the first step when performing accurate CAA (Computational Aero-Acoustics)
The lectures will be given on-line (Live) using Zoom. During the workshops, the participants will get supervision in a joint Zoom room which will enable participants to learn from each others questions. Part of the supervision may also be given in individual break-out Zoom rooms.
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Lectures will be given in the mornings; in the afternoons there will be workshops using Python (recommended) , Matlab or Octave. The participants must have a PC/Mac/Desktop with one of these software installed. In the workshops, the participants will use Python/Matlab/Octave for analyzing analyzing SGS models, SAS, PANS, DES and DDES. Scripts will be use for generaring isotropic and anistropic (non-isotropic) synthetic turbulent fluctuations for inlet boundary conditions and embedded LES.
The number of participants is limited to 16.



The development of computers and Computational Fluid Dynamics (CFD) has made the numerical simulation of complex fluid flow, combustion, aero-acoustics and heat transfer problems possible. Turbulent flow in three-dimensional, complex geometries -- unsteady or steady -- can be dealt with.
Presently CFD methods can replace, or complement, many experimental methods; we can use a numerical wind tunnel instead of an experimental one.
Today, most CFD simulations are carried out with traditional RANS (Reynolds-Averaged Navier-Stokes). In RANS, we split the flow variables into one time-averaged (mean) part and one turbulent part. The latter is modelled with a turbulence model such as k-eps or Reynolds Stress Model.
For many flows it is not appropriate to use RANS, since the turbulent part can be very large and of the same order as the mean. Examples are unsteady flow in general, wake flows or flows with large separation. For this type of flows, it is more appropriate to use Large Eddy Simulation (LES). In order to extend LES to high Reynolds number flows new methods have recently been developed. These are called DES (Detached Eddy Simulation), URANS (Unsteady RANS), PITM (Partially Integrated Transport Model), PANS (Partially Averaged Navier-Stokes) or Hybrid LES-RANS. They are all unsteady methods and they are a mixture of LES and RANS.
In aero-acoustics the noise is generated by turbulence. The best way to accurately predict large-scale turbulence is to carry out an unsteady simulation of the flow field (i.e. LES, DES, hybrid LES-RANS or URANS). After that the noise is predicted separately in CAA (Computational Aero-Acoustics) in which the large-scale turbulence is used in analogy methods based on Lighthill, Kirchhoff or Ffowcs Williams.
In LES, DES, URANS and Hybrid LES-RANS the large-scale part of the turbulence is solved for by the discretized equations whereas the small-scale turbulence is modelled. The definition of ''large-scale'' varies in the different methods. Furthermore, the limit between ''large-scale'' and ''small-scale' is often not well defined. Since turbulence is three-dimensional and unsteady, it means that in all the methods the simulations must always be carried out as 3D, unsteady simulations.





The course will give an introduction to LES, DES, hybrid LES-RANS and unsteady RANS. During the lectures we will discuss the theory and during the workshops We will use simple Python (recommended) , Matlab or Octave. programs to gain detailed insight in various numerical and modelling aspects. The participants must have access to a PC/Mac/Desktop with on of these three programs installed.
The number of participant is limited to 16
We will address questions like:
  • how should I make my mesh?
  • why should I in LES use a dissipative discretization scheme?
  • is it necessary to used central differencing in DES and URANS?
  • what is the difference between LES and unsteady RANS?
  • what turbulence models can I use in DES and unsteady RANS?
  • what fk values are suitable in PANS?
  • to enhance numerical stability, can a turbulence model with high dissipation be used?
  • how do I prescribe inlet boundary conditions?
  • inlet boundary conditions: can I use steady conditions? which is best, synthesized turbulence or a pre-cursor DNS? Download Python/Matlab/Octave files for generating synhetic inlet fluctuations
In the workshop, we will learn how to interpretate results from an unsteady simulation. We will evaluate and compare the two types of turbulent stresses, i.e. the resolved stresses and the modelled stresses (more detail at the bottom). When doing LES-URANS/DES, you have to ask yourself similar questions as when doing measurements:
  • when is the flow fully developed so that I can start time-averaging?
  • for how long time do I need to time-average?
  • is it enough if I get accurate mean flow or do I also need accurate resolved turbulent stresses?
  • how do I estimate the quality of my LES or hybrid LES-RANS? Spectra? 2-point correlations? SGS dissipation? For more info, see QLES 2009 and references
The most important drawback/bottleneck of LES is the requirement to use very fine grid near walls. The grid must be fine in all directions, not only the wall-normal direction. Much of the research on LES is today focused in getting around this bottleneck. One approach is hybrid LES-RANS. In this method RANS is used near walls and LES is used in the remaining part of the domain. In the afternoon of Day 2 some hybrid LES-RANS methods (including the SAS model) will be presented and discussed.
Inlet boundary conditions are much more difficult in LES and hybrid LES-RANS than in RANS. In RANS it is sufficient to prescribe time-averaged profiles. In LES and hybrid LES-RANS unsteady, turbulent fluctuations must be supplied. One alternative is to do a pre-cursor DNS and store data at a cross-sectional plane on disc which can be read in the subsequent LES or hybrid LES-RANS simulation. Another alternative is to use synthesized turbulence. The participants will during the last workshop (Day 3) have the opportunity to learn how to to create synthesized turbulence using Python/Matlab/Octave.
Synthetic turbulent fluctuations are also important in Embedded LES in which an LES/DES region is embedded in a steady or unsteady RANS region. Usually the upstream region is a RANS region and the downstream region is LES or DES. Turbulent fluctuations must be added at the interface between RANS and LES to ensure a rapid transition from steady RANS where all turbulence is modelled to LES/DES where most of the turbulence is resolved.




The participants will be given an introduction to LES, DES, hybrid LES-RANS and unsteady RANS. We expect many participants to be first-year PhD students or users of in-house CFD codes or commercial CFD packages for traditional RANS simulations. This course will give the required knowledge to do CFD predictions using also unsteady methods.




We believe that the course will be useful for engineers and PhD students working with problems including pure fluid flow, aero-acoustics, combustion and heat transfer in industry as well as at universities.
The participants must have access to a PC/Mac/Desktop with Python (recommended), Matlab or Octave installed.
The number of participants is limited to 16.





The lecturer at the course (both during lectures and workshops) will be Prof. Lars Davidson, Chalmers University of Technology.
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  • L. Davidson, eBook (Opens a PDF file, Chapters 18 - 27)




The course material is in English and the lectures will be given in English.




The course will be held 5, 7, 9 December 2022 on Zoom. and is organized by Flowsim AB.





Registration form should be submitted no later than November 11, 2022.
The price is 14,700 SEK (excl. VAT) which includes course material. For PhD students employed at universities the fee is reduced to 12,400 SEK (excl. VAT). No refunding after November 11. The number of participants is limited to 16.
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DAY 1, Monday (9.00 -- 17.00)

  • Introduction to Large Eddy Simulation
  • Filtering of the equations; discretization convection schemes for LES, SGS models.
  • Workshop: interpretation of results from a LES and unsteady RANS. Time-averaging, evaluation of various forms of turbulent stresses etc.

Tueday (no teaching). Participants can work on assignments

DAY 2, Wednesay (9.00 -- 17.00)

  • Dynamic SGS models, scale-similarity models, transport equations for SGS stresses
  • Introduction to DES, URANS, PANS and SAS
  • Introduction to hybrid LES-RANS
  • Workshop continued: explicit filtering, SGS models, spectra, two-point correlations, viscous and SGS dissipation, scale-similarity models, DES, DDES and SAS

Thursday (no teaching). Participants can work on assignments

DAY 3, Friday (9.00 -- 17.00)

  • Inlet boundary conditions: prescribed spectra, integral length scale, integral time scale, implementation of inlet boundary conditions in your LES/DES code
  • Workshop: generate synthetic isotropic and anistropic (non-isotropic) inlet boundary conditions with Python/Matlab/Octave scripts
  • PANS and embedded LES
  • Synthetic isotropic and anistropic (non-isotropic) turbulent fluctuations for embedded LES
  • Workshop: analysis of PANS and embedded LES




  1. L. Davidson, "How to generate synthetic turbulent inlet fluctuations"
    Download Python/Matlab scripts
  2. L. Davidson and S.-H. Peng
    "A Hybrid LES-RANS Model Based on a One-Equation SGS Model and a Two-Equation k-omega Model", The Second International Symp. on Turbulence and Shear Flow Phenomena, Eds: E. Lindborg, A. Johansson, J. Eaton, J. Humphrey, N. Kasagi, M. Leschziner, M. Sommerfeld, Vol. 2, pp. 175-180, Stockholm, 2001.
    View PDF file
    Hybrid LES-RANS: A Combination of a One-Equation SGS Model and a k-omega Model for Predicting Recirculating Flows" ECCOMAS Computational Fluid Dynamics 2001 Conference, Swansea, UK, 2001.
    View PDF file
  4. L. Davidson and S.-H. Peng
    "Hybrid LES-RANS: A one-equation SGS Model combined with a k-omega model for predicting recirculating flows", Int. J. Num. Meth. in Fluids, Vol. 43, pp. 1003-1018, 2003.
  5. S. Dahlström and L. Davidson
    "Hybrid RANS/LES employing Interface Condition with Turbulent Structure", Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Report, Göteborg, Sweden, 2003
    View PDF file
  6. S. Dahlström and L. Davidson
    "Hybrid RANS-LES with Additional Conditions at the Matching Region", Turbulence Heat and Mass Transfer 4, pp. 689-696, K. Hanjalic, Y. Nagano and M.J. Tummers (eds.), begell house, inc., New York, Wallingford (UK), 2003.
    View PDF file
  7. L. Davidson and S. Dahlström
    "Hybrid RANS-LES: an Approach to make LES Applicable at High Reynolds Number", CHT-04: Advances in Computational Heat Transfer III, Keynote Lecture, G. de Vahl Davis and E. Leonardi (eds.), Norway, April 2004 (updated version in International Journal of Computational Fluid Dynamics, Vol. 19, No. 6, pp 415-427 2005, see below).

  8. L. Davidson and S. Dahlström
    "Hybrid RANS-LES: an Approach to make LES Applicable at High Reynolds Number", Int. J. of Comp. Fluid Dynamics Vol. 19, No. 6, pp 415-427, 2005.
  9. L. Davidson and M. Billson, "Hybrid LES/RANS Using Synthesized Turbulence for Forcing at the Interface", ECCOMAS 2004, P. Neittaanmaki, T. Rossi, S. Korotov, E. Onate, J. Periaux, and D. Knorzer (eds.), July 24-28, Finland.
    View PDF file
  10. L. Davidson and S. Dahlström
    "Hybrid LES-RANS: Computation of the Flow Around a Three-Dimensional Hill", Engineering Turbulence Modelling and Measurements - ETMM6, Sardinia, Italy, May 23-25, 2005.
    View PDF file
  11. C. Wollblad and L. Davidson
    "POD based reconstruction of subgrid stresses for wall bounded flows using neural networks", 5th International Symposium on Turbulence, Heat and Mass Transfer, Dubrovnik, Croatia, September 25-29, 2006.
    View PDF file
  12. C. Wollblad and L. Davidson
    "POD based reconstruction of subgrid stresses for wall bounded flows using neural networks", Flow, Turbulence and Combustion, Vol. 81, No. 1-2, pp. 77-96, 2008.
    Go to journal
  13. L. Davidson
    "Evaluation of the SST-SAS Model: Channel Flow, Asymmetric Diffuser and Axi-symmetric Hill", ECCOMAS CFD 2006, September 5-8, 2006, Egmond aan Zee, The Netherlands, 2006.
    View PDF file
  14. L. Davidson
    "Transport Equations in Incompressible URANS and LES", Rept. 2006/01, Division of Fluid Dynamics, Dept. of Applied Mechanics, Dynamics, Chalmers University of Technology Göteborg, 2006.
    View PDF file
  15. L. Davidson
    "Using Isotropic Synthetic Fluctuations as Inlet Boundary Conditions for Unsteady Simulations" Advances and Applications in Fluid Mechanics, Vol. 1(1), pp. 1-35, 2007.
  16. L. Davidson
    " Hybrid LES-RANS: Estimating Resolution Requirements Using Two-Point Correlations and Spectra", ERCOFTAC Bullentin, Special Issue on Wall modelling in LES, pp. 19--24, March, 2007. (corrected)
    View PDF file
  17. L. Davidson
    A dissipative scale-similarity model, DLES7: Direct and Large-Eddy Simulations 7, 8-10 Sept 2008, Trieste, 2008.
    View PDF file
  18. L. Davidson
    "Hybrid LES-RANS: back scatter from a scale-similarity model used as forcing", Phil. Trans. of the Royal Society A, Vol. 367, Issue 1899, pp. 2905-2915, 2009.
  19. J. Ask and L. Davidson
    "A Numerical Investigation of the Flow Past a Generic Mirror and its Impact on Sound Generation", Journal of Fluids Engineering, vol.131, number 061102, 2009.
  20. L. Davidson
    "Large Eddy Simulations: how to evaluate resolution", International Journal of Heat and Fluid Flow, Vol. 30(5), pp. 1016-1025, 2009.
    Get article at publisher's www page
    View PDF file of manuscript
  21. L. Davidson
    Fluid mechanics, turbulent flow and turbulence modeling, course material in MSc courses, Division of Fluid Dynamics, Dept. of Applied Mechanics, Chalmers University of Technology, Göteborg, 2010
    View PDF file
  22. J. Ma, S.-H. Peng, L. Davidson and F. Wang
    A Low Reynolds Number Partially-Averaged Navier-Stokes Model for Turbulence, 8th International ERCOFTAC Symposium on Engineering Turbulence, Modeling and Measurements, Marseille, France, 9-11 June, 2010.
    View PDF file
  23. J. Ask, L. Davidson
    Flow and Dipole source evaluation of a generic SUV,J. Fluids Eng., Vol. 132, No. 051111, 2010.
  24. J. Ask, L. Davidson
    A Numerical Investigation of the Flow Past a Generic Side Mirror and its Impact on Sound Generation,J. Fluids Eng., Vol. 131, No. 061102, 2009.
  25. L. Davidson
    "How to estimate the resolution of an LES of recirculating flow", Quality and Reliability of Large-Eddy Simulations II, Ercoftac Series, Springer, 2010.
    View PDF file
  26. Ma, J.M, S.-H. Peng, L. Davidson and F.J. Wang
    A low Reynolds number variant of partially-averaged Navier-Stokes model for turbulence, Int. J. Heat Fluid Flow, Vol. 32, pp. 652-669, 2011.
    Get article at publisher's www page
    View PDF file of manuscript
  27. L. Davidson and S.-H. Peng
    "Embedded LES Using PANS", I6th AIAA Theoretical Fluid Mechanics Conference, AIAA paper 2011-3108, 27 - 30 Jun 2011, Honolulu, Hawaii.
    View PDF file
  28. L. Davidson
    "A New Approach of Zonal Hybrid RANS-LES Based on a Two-equation k-eps Model", ETMM9: International ERCOFTAC Symposium on Turbulence Modelling and Measurements, Thessaloniki, Greece, 2012
    View PDF file
  29. L. Davidson
    "Large Eddy Simulation of Heat Transfer in Boundary Layer and Backstep Flow Using PANS", Turbulence, Heat and Mass Transfer 7 Hanjalic, Y. Nagano, D. Borello and S. Jakirlic (Editors), Begell House, Inc., 2012
    View PDF file
  30. L. Davidson and S.-H. Peng
    "Embedded Large-Eddy Simulation Using the Partially Averaged Navier-Stokes Model", AIAA J, Vol. 51(5), pp. 1066-1079, 2013.
    View PDF file
  31. L. Davidson
    "Backscatter from a scale-similarity model: embedded LES of channel flow, developing boundary layer flow and backstep flow", 8th International Symposium on turbulence and shear flow phenomena (TSFP8), Poitiers, France, 28-30 August 2013
    View PDF file
  32. L. Davidson
    "The PANS k-eps model in a zonal hybrid RANS-LES formulation", International Journal of Heat and Fluid Flow, pp. 112-126, vol. 46, 2014.
    View PDF file of manusctip
    Get PDF file from publisher
  33. L. Davidson and C. Friess, The PANS and PITM model: a new formulation of f_k, Proceedings of 12th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM12), Montpelier, France 26-28 September, 2018
    View PDF file
  34. L. Davidson, Zonal Detached Eddy Simulation coupled with steady RANS in the wall region, ECCOMAS MSF 2019 Thematic Conference, 18-20 September 2019, Sarajevo, Bosnia-Herzegovina.
    View PDF file
  35. L. Davidson, "Non-Zonal Detached Eddy Simulation coupled with a steady RANS solver in the wall region", ERCOFTAC Bullentin 120, Special Issue on Current trends in RANS-based scale-resolving simulation methods, pp. 43-48, 2019. View PDF file
  36. L. Davidson and Ch. Friess, "Detached Eddy Simulations: Analysis of a limit on the dissipation term for reducing spectral energy transfer at cut-off", ETMM13: The 13th International ERCOFTAC symposium on engineering, turbulence, modelling Rhodes, Greece, 15-17 September, 2021
    View PDF file
  37. L. Davidson
    "Detached Eddy Simulation coupled with steady RANS in the wall region", ETMM13: The 13th International ERCOFTAC symposium on engineering, turbulence, modelling Rhodes, Greece, 15-17 September, 2021
    View PDF file





Please contact
Lars Davidson
tel. 46 (0) 730-791 161,
E-mail: lada@flowsim.se, lada@chalmers.se