Implementation of the $\varphi - f $ - DDES model in Code_Saturne

This page contains the equations necessary for the implementation of the $\varphi -f$ DDES model into Code Saturne v2.0.1.

See A hybrid numerical scheme for a new formulation of delayed detached-eddy simulation (DDES) based on elliptic relaxation, N. Ashton, A. Revell, R. Prosser, Journal of Physics: Conference Series, 13th European Turbulence Conference, Vol. 318, (2011)

See Spalart, P.R. et al. A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities. Theoretical and Computational Fluid Dynamics 20, 181-195(2006).

Laurence, D L, Uribe, J C & Utyuzhinkov, S V 2004 A robust formulation of the v2 − f model. Flow Turbulence and Combustion 73, 169185.

Source term for $k$ equation

Destruction term in the $k$ equation

  \begin{equation*} \varepsilon = \varphi \frac{k^{3/2}}{L_{DDES}} \end{equation*}(1)

Where the function $L_{DDES}$ is:

  \begin{equation*} L_{DDES} = L_{RANS} -f_{d}\max\left(0,L_{RANS}-L_{LES}\right) \quad , \quad f_{d} = 1 - \tanh\left(\left[8\frac{\nu_{t}+\nu}{\sqrt{U_{i,j}U_{i,j}}\kappa^{2}y^{2}}\right]^{3}\right)  \end{equation*}(2)

The length scales are:

  \begin{align*} L_{RANS} \ &= \ \varphi \frac{k^{3/2}}{\varepsilon} & L_{LES} \ & = \ \Psi C_{DDES}\Delta & \Psi = \left(\frac{C_{\varepsilon 1}^{'}}{C_{\varepsilon 2}}\right)^{3/4}\left(\varphi\right)^{1/4} \\ \end{align*}(3)

Where, $\kappa = 0.41$, $C_{DDES} = 0.60$ and $d_{w}$ is the distance to the wall

Decaying Isotropic Turbulence (DIT)


Modified Code_Saturne v2.0.1 subroutines


  • include and define the index values , IDDES, which turns off the change in K transport equation if it is equals to zero and enables it when it is 1 or 2 depending on the formulation.
  • include and define $C_{DDES}$.


  • Extra memory is required for the storage of the wall distance and $\sqrt{U_{i,j}U_{i,j}}$. The call headers need to be changed to include extra working arrays, W10 and W11.

  • W10 and W11 defined as double precision.

The DDES model will run using an index argument, where if IDDES.EQ.2 then the DDES modification will be used.

  • Working array W10 is $\sqrt{U_{i,j}U_{i,j}}$

  • Working array W11 is $d_{w}$

Source terms

  • Calculate $L_{RANS}$.

  • Calculate $r_{d}$

  • Calculate $f_{d}$

  • Calculate $L_{DDES}$

  • Add an if statement to the $k$ equation, where if IDDES.Eq.2 then the $\varepsilon$ becomes $\varphi \frac{k^{3/2}}{L_{DDES}}$


  • Change memkep call to include extra working arrays W10 and W11

  • Change call to turbke, to include extra working arrays W10 and W11


  • Add extra working arrays, IW10, IW11

  • Change definitions, integers for IW10, IW11

  • Change memory pointers to include new working arrays


  • Change INEEDY IF statement to include the v2f model. i.e ITURB = 50 to calculate the distance to the wall


  • set default value, IDDES = 0

  • include incddes.h

  • include default values for $C_{DDES}$


  • IDDES = 0
  • $C_{DDES}$ = 0.60
  • include incddes.h


  • include incddes.h
  • Include printout for IDDES
  • include printout for $C_{DDES}$


  • include incddes.h
  • include an IF statement to check that SAS and DDES cannot run at the same time.

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pdfpdf cddes_phif_etc.pdf manage 151.2 K 2011-06-21 - 20:47 NeilAshton Cddes calibration for the phif DDES model
Topic revision: r4 - 2012-04-28 - 21:27:03 - NeilAshton
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18 Mar 2019


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