Unsteady Simulations:
LES, DES, hybrid LES/RANS and Machine Learning
26, 28, 29 October 2026

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A three-day online course
on
Unsteady Simulations:
LES, DES, hybrid LES/RANS and Machine Learning

 
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. Day 3, an introduction will be given on how to use Machine Learning for improving underlying RANS turbulence models [41, 42] and wall-functions [38-40].
 
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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A numwer of lectures will be given every day followed by will be workshops using →Python. The participants must have a PC/Mac/Desktop with Python installed. In the workshops, the participants will use Python for →analyzing SGS models, SAS, PANS, DES, and DDES. These will be the topics Day 1 and 2.
 
Day 3 is devoted to Machine Learning. Neural network and KDTRee in Python's Pytorch will be used to inmprove RANS/LES turbulence models and wall functions.
 
The number of participants is limited to 16.
 

 
 

BACKGROUND

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.
 


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THE COURSE

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 scripts to gain detailed insight in various numerical and modelling aspects. The participants must have access to a PC/Mac/Desktop with Python installed.
 
The number of participant is limited to 16
 
 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. 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. Day 2 some hybrid LES-RANS methods (including the SAS model) will be presented and discussed.
 


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OBJECT

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.
 


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PARTiCiPANTS

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.
 
 

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LECTURER

The lecturer at the course (both during lectures and workshops) will be →Prof. Lars Davidson, Chalmers University of Technology.
 
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COURSE MATERiAL

  • L. Davidson, →eBook (Opens a PDF file, Chapters 18 - 27)



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COURSE LANGUAGE

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


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LOCATiON

The course will be held 26, 28, 29 October 2026 on →Zoom. and is organized by Flowsim AB.
 

 

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REGiSTRATiON

Registration form should be submitted no later than October 2, 2026.
 
The price is 14,700 SEK (excl. VAT) which includes course material. The number of participants is limited to 16.
 
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PROGRAM



The course will include three lectures (45 minutes) and four workshops (45 minures) every day. The time when the first lecture starts will be determined so that it fits all participants as well as possible. This time will be set when the invoices are sent to the participants.

DAY 1, Monday

  • 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

  • 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

DAY 3, Thursday

  • Introduction to Machine Learning for improving turbulence models [40-42]
  • Workshop: Machine Learning for turbulence modeling (Neural Network in Pytorch) using Python
  • Introduction to Machine Learning for improving wall functions [38-40]
  • Workshop: Machine Learning for turbulence modeling (Neural Network and KDTree in Pytorch) using Python

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PUBLiCATiONS

  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
     
  3. L. DAVIDSON
    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 manusctipt
    →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
     
  38. L. Davidson
    "Using Machine Learning for formulating new wall functions for Large Eddy Simulation: A First Attempt", Div. of Fluid Dynamics, Mechanics and Maritime Sciences, Chalmers University of Technology, 2022.
    →View PDF file
     
  39. L. Davidson
    "Using Machine Learning for formulating new wall functions for Large Eddy Simulation: A Second Attempt", Div. of Fluid Dynamics, Mechanics and Maritime Sciences, Chalmers University of Technology, 2022.
    →View PDF file
     
  40. L. Davidson
    "Using Machine Learning for formulating new wall functions for Detached Eddy Simulation", ERCOFTAC symposium on Engineering, Turbulence, Modelling and Measurements (ETMM14), in Mini-Symposium: Machine learning for turbulence, Barcelona, Spain 6th - 8th September 2023; Chalmers University of Technology, 2022.
    →View PDF file
     
  41. L. Davidson
    "Using Machine Learning for Improving a Non-Linear k-eps Model: A First Attempt", Div. of Fluid Dynamics, Mechanics and Maritime Sciences, Chalmers University of Technology, 2023.
    →View PDF file
     
  42. L. Davidson
    "Using Neural Network for Improving an Explicit Algebraic Stress Model in 2D Flow", CUSF 2024, Proceedings of the Cambridge Unsteady Flow Symposium", Springer, Editors: J. C. Tyacke and N. R. Vadlamani, 2024 (to appear)
    →View presentation
    →View PDF file
    →Proceedings
    →Download code

  43. L. Davidson
    "Hybrid LES/RANS for flows including separation: A new wall function using Machine Learning based on binary search trees", Journal of Turbulence, 2025. →Get article at publisher
    →Download Python script and databases

  44. L. Davidson
    "Using Physical Informed Neural Network (PINN) to Improve a k-omega Turbulence Model", ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM-15), Dubrovnik on 22-24 September 2025.
    →Download Python script and databases

  45. L. Davidson
    "Understanding Autograd and Neural Network in PyTorch", Div. of Fluid Dynamics, Mechanics and Maritime Sciences, Chalmers University of Technology, 2025.
    Download paper

  46. L. Davidson
    "Using Physics Informed Neural Network (PINN) and Neural Network (NN) to Improve a k-omega Turbulence Model", Journal of Turbulence, https://doi.org/10.1080/14685248.2026.2665148, vol. 27, issue 7, pp. 187--208, 2026 →Download paper, Python scripts and CFD codes


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QUESTiONS & FURTHER iNFORMATiON



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

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