Implementation of EBRSM - DDES model in Code_Saturne

This page contains the equations necessary for the implementation of the EBRSM - DDES model into Code Saturne.

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).

Manceau R et al. Elliptic Blending model: A new near-wall Reynolds-stress turbulence closure. Physics of Fluids, 14, 744-754(2001)

Source terms for $R_{ij}$ equation

The dissipation term of the $R_{ij}$ equations becomes:

$\varepsilon_{ij} = (1-Ak\alpha)\frac{u_{i}u_{j}}{k}\frac{k^{3/2}}{L_{ddes}} + Ak\alpha \frac{2}{3}\frac{k^{3/2}}{L_{ddes}}\delta_{ij}$

The length scale used in a DDES formulation is a switch between the RANS length scale and a LES length scale formulation:

$L_{DDES} = L_{RANS} - f_{d} max \left(0,L_{RANS} - L_{LES}\right)$

The LES Length scale is:

$ \\ L_{LES} = C_{DDES}\Delta$

The RANS length scale is defined as:

$ \\ L_{RANS} = \frac{k^{3/2}}{\epsilon}$

Where $k$ is:

$ \\ k = 0.5 (u^{'}u^{'}+v^{'}v^{'}+w^{'}w^{'})$

The function $f_{d}$ is:

$ \\ f_{d} = 1 - tanh\left(\left[8r_{d}\right]^{3}\right)$

$ \\ r_{d} = \frac{\nu_{t} + \nu}{\sqrt{U_{i,j}U_{i,j}}\kappa^{2}d_{w}^{2}}$

Where, $\kappa = 0.42$ and $d_{w}$ is the distance to the wall

Decaying Homogeneous Isotropic Turbulence (DHIT) EBRSM- DDES

Modified Code_Saturne v1.4 subroutines


  • include and define the index values , IDDES which turns off the change in dissipation transport equation if it is equals to zero and enables it when it is one.
  • include and define $C_{DDES}$


  • IDDES = 0
  • $C_{DDES}$ = 0.65
  • include incddes.h


  • set default value, IDDES= 0,

  • include incddes.h

  • include default values for $C_{DDES}$


  • allocate new memory for gradient calculations, W10 and W11

  • Define W10,W11 as double precision

  • 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 $F_{DDES}$

  • Add an if statement to the $k$ equation, where if IDDES.Eq.1 the change in $\varepsilon_{ij}$ will be switched on


  • Include new working arrays, W10, W11 in the call to resebm
  • Define W10 and W11 as double precision


  • Change INEEDY IF statement to include ITURB = 32 to calculate the distance to the wall


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

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Topic revision: r6 - 2010-10-27 - 14:00:26 - NeilAshton
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25 Mar 2019


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