3 day
22, 24, 26 June 2020

Large-Eddy Simulation
Detached-Eddy Simulations
How to use an in-House Fortran source code

The traditional method for CFD in industry and universities is Reynolds-Averaged Navier-Stokes (RANS). It is a fast method and mostly rather accurate. However, in flows involving large separation regions, wakes and transition it is inaccurate. The reason is that all turbulence is modeled with a turbulence model. For predicting aeroacoustic, RANS is even more unreliable. For these flow, Large-Eddy Simulation (LES) and Detached-Eddy Simulations (DES) is a suitable option although it is much more expensive. Still, in many industries (automotive, aerospace, gas turbines, nuclear reactors, wind power) DES is used as an alternative to RANS. In universities, extensive research has been carried out during the last decade(s) on LES and DES.
Unfortunately, most engineers and many researchers have limited knowledge of what a LES/DES CFD code is doing. The object of this on-line course is to close that knowledge gap. During the course, the participants will learn and work with an in-house LES/DES code called CALC-LES, written by the lecturer. It is a finite volume code written in Fortran 77. It includes two zero-equation SGS models (Smagorinsky and WALE) and one two-equation model (the PANS model). The convective terms in the momentum equations are discretized using central differencing. Hybrid central/upwind is used for the k and eps equations. The Crank-Nicolson scheme is used for time discretization of all equations. The numerical procedure is based on an implicit, fractional step technique with a multigrid pressure Poisson solver [1] and a non-staggered grid arrangement. CALC-LES is a single-block structured code. It is not parallelized. However, it is very fast. The hump flow (see below), it requires less than 14 seconds/time step on a standard PC. For a converged solutions, 7500+7500 time-steps are sufficient. The number of cells is 648x108x64.


The course includes lectures (12 hours) and workshops (12 hours) learning and using CALC-LES. The course is given 22, 24, 26 June 2020.
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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In the lectures we will address:
  • finite volume discretization
  • central differencing scheme
  • hybrid central/upwind scheme
  • Smagorinsky model
  • WALE model
  • the k-eps DES model
  • two-equation PANS model (k and epsilon)
  • wall and periodic boundary conditions
  • TDMA (tri-diagonal-matrix-algorithm) solver
  • how to prescribe turbulent inlet boundary conditions
  • how to generate inlet anisotropic synthetic turbulent fluctuations

In the workshops, the participants will use CALC-LES.
The participants will get the source code and install it on their lap-top or desk-top. It is recommended that the participants use Linux with the GNU, Intel's or PGI compiler and have a simple plotting program such as Python, Matlab or Octave installed. If participants use Windows or Mac, no support will be given for installing the code (it is most likely easy to install the code also on Windows and Mac).
Four test cases are provided in the CALC-LES code:
  1. DNS and LES of fully developed channel flow [2-5]. Periodic boundary conditions in streamwise and spanwise directions.


  2. LES of atmospheric boundary layer over a forest relevant to windpower engineering [10,11]. Periodic boundary conditions in streamwise and spanwise directions. The figure show instantanoues streamwise velocity. The height of the forest (20m) is indicted by the green line. A 384x192x96 mesh is used. The CPU time for one timestep on a standard desktop PC is 15 seconds.

  3. LES of the hill flow [6]. Periodic boundary conditions in streamwise and spanwise directions.

  4. DES of the hump flow [6]. Synthetic inlet fluctuations at the inlet [7-9]. Periodic boundary conditions spanwise direction. On a 624x108x64 mesh the CPU time is 20 seconds per time step on a standard PC [14].
    Python and Matlab/Octave files



The object is that the participants should learn how a CFD code for LES/DES works. It will give them increased knowledge, confidence and know-how when using commercial CFD codes.


The participants are expected to hold a MSC degree or PhD degree related to fluid mechanics. They are expected to have at least a basic knowledge in LES and DES. Programming skills is also useful. The course is expected to be valuable also for researchers with extensive knowledge in LES and/or DES. The participants may continue to use CALC-LES after the course, in their daily work and/or research. However, no support will be given.


The lecturer at the course (both during lectures and workshops) will be Prof. Lars Davidson, Chalmers University of Technology.
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The course material is in English and the lectures will be given in English.


The course will be held 22, 24, 26 June 2020 online at Zoom
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Registration form should be submitted no later than May 20, 2020. The price is 14,700 SEK (excl. VAT). No refunding after May 21. The number of participants is limited to 16.
registration form


DAY 1, Monday, 8 hours

  • General structure of CALC-LES
  • Discretization in CALC-LES
  • Compute geometrical quantities
  • Studying Test Case 1 (channel flow)
  • Studying Test Case 2 (atmospheric boundary layer)
  • WORKSHOP, see Section workshop in CALC-LES: A Fortran Code for LES and Hybrid LES-RANS
    • Fully-developed channel flow simulations using PANS
    • Channel flow simulations with inlet-outlet using PANS
    • Investigation of different synthetic fluctuating inlet fluctuations. For example, change the prescribed integral length scale, the integral time scale, the anisotropy ...

Tueday (no teaching). Participants can work on CALC-LES

DAY 2, Wednesday, 8 hours

  • Implicit Rhie-Chow interpolation in CALC-LES
  • TDMA solver
  • Implementation of Zero equation models
  • Implementation of the PANS model in CALC-LES
  • Studying Test Case 3 (hill flow)
  • WORKSHOP, see Section workshop in CALC-LES: A Fortran Code for LES and Hybrid LES-RANS
    • Implementing a one-equation hybrid LES-RANS model
    • Implementing a DES model (k-eps and/or k-omega)
    • Implementing a DDES model (k-eps and/or k-omega)

Thursday (no teaching). Participants can work on CALC-LES

DAY 3, Friday, 8 hours

  • How to implement a new turbulence model in CALC-LES
  • Implementation of synthetic turbulence in CALC-LES
  • How to generate anisotropic turbulent fluctuations in CALC-LES
  • how to implement a k-eps DES model
  • Pre-cursor RANS (using a 1D solver written in Python and Matlab/Octave) as input to synthetic turbulence generator
  • Studying Test Case 4 (hump flow)
  • WORKSHOP, see Section workshop in pdf
    • Implementing an IDDES model (k-eps and/or k-omega)
    • Implementing the SAS model (k-omega)
    • Making heat transfer simulations in a channel with inlet-outlet boundary conditions

Above, we give above examples on what turbulence models to implement in the workshops. Students may of course propose to implement other turbulence models.


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



  1. P. Emvin, The Full Multigrid Method Applied to Turbulent Flow in Ventilated Enclosures Using Structured and Unstructured Grids. PhD thesis, Dept. of Thermo and Fluid Dynamics, Chalmers University of Technology, Göteborg, 1997.
  2. L. Davidson, Large eddy simulations: how to evaluate resolution. International Journal of Heat and Fluid Flow, 30(5):1016-1025, 2009.
  3. L. Davidson, The PANS k-ε model in a zonal hybrid RANS-LES formulation. International Journal of Heat and Fluid Flow, 46:112-126, 2014.
  4. L. Davidson, Zonal PANS: evaluation of different treatments of the RANS-LES interface. Journal of Turbulence, 17(3):274-307, 2016.
  5. A. Altintas and L. Davidson, Direct numerical simulation analysis of spanwise oscillating lorentz force in turbulent channel flow at low Reynolds number. Acta Mechanica, pages 1-18, 2016.
  6. J. Ma, S.-H. Peng, L. Davidson, and F. Wang, A low Reynolds number variant of Partially-Averaged Navier-Stokes model for turbulence. International Journal of Heat and Fluid Flow, 32(3):652-669, 2011.10.1016/j.ijheatfluidflow.2011.02.001.
  7. L. Davidson, Using isotropic synthetic fluctuations as inlet boundary conditions for unsteady simulations. Advances and Applications in Fluid Mechanics, 1(1):1-35, 2007.
  8. L. Davidson and S.-H. Peng, Embedded large-eddy simulation using the partially averaged Navier-Stokes model. AIAA Journal, 51(5):1066-1079, 2013.
  9. L. Davidson, Two-equation hybrid RANS-LES models: A novel way to treat k and ω at inlets and at embedded interfaces. Journal of Turbulence, 18(4):291-315, 2017.
  10. B. Nebenfuhr, L. Davidson, Large-Eddy Simulation Study of Thermally Stratified Canopy Flow, Boundary-Layer Meteorology, Vol. 156, number 2 , pp. 253-276, 2015
  11. B. Nebenfuhr, L. Davidson, Prediction of wind-turbine fatigue loads in forest regions based on turbulent LES inflow fields, Volume 20, Issue 6 pp. 1003-1015, Wind Energy, 2017.
  12. 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
  13. 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
  14. L. Davidson, inlet boundary conditions.
  15. 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.