Implementation of the SST - SAS model in Code_Saturne

This page contains the equations necessary for the implementation of the $k-\omega$ SST - SAS model into Code Saturne v2.0.1.

See Menter F. R.,Egorov Y. (2005) A Scale-adaptive simulation model using two-equation models. AIAA paper 2005-1095.

Source term for $\omega$ equation

$Q_{SAS}=max \left[\rho\zeta_{2}kS^{2} \left ( \frac{L}{L_{\nu K}} \right )^{2} - C . \frac{2\rho k}{\sigma_{\phi}} max \left (\frac{\mid \nabla\omega \mid^{2}}{\omega^{2}},\frac{\mid\nabla k \mid^{2}}{k^{2}}\right ), 0 \right]$

The coefficients are:

$\zeta_{2} = 3.51$ $\sigma_{\phi} = 2/3$ $C = 2$

Where $L$ is the modelled turbulence length scale

$L = \sqrt{k}/\left (c_{\mu}^{\frac{1}{4}}.\omega \right )$

The von Karman Length Scale $L_{\nu k}$ is as follows:

$ \\ L_{v k} = \frac {k S}{\mid \nabla^{2} U \mid}$

The second velocity derivative is:

$\\ \mid \nabla^{2} U \mid = \sqrt{(\nabla^{2}U)^{2} + (\nabla^{2}V)^{2} + (\nabla^{2}W)^{2}} \\ \nabla^{2} = \frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}} + \frac{\partial^{2}}{\partial z^{2}} $

Limiter for the $L_{\nu k}$ :

$L_{vK} \ = \ max \left ( \frac{\kappa S}{\mid \nabla^{2}\mathbf{U} \mid} , L_{vK}^{min} \right )$

$L_{vK}^{min} \ = \ C_{S}\cdot \sqrt{\frac{\zeta_{2}\kappa}{\left ( \beta /c_{\mu}\right ) - \alpha}} \cdot \Delta$

Decaying Homogeneous Isotropic Turbulence (DHIT)


Modified Code_Saturne v2.0.1 subroutines


  • include and define the index, ISAS, which turns off the SAS source term if it is equals to zero and enables it when it is one.
  • include and define $C_{SAS}$ and $\zeta_{2}$ .


  • Extra memory is required for the calculations of the magnitude of the gradients of $k$ and $\omega$. The call headers need to be changed to include extra working arrays, W10 and W11.

  • W10 and W11 defined as double precision.

The SAS model will run using an index argument, where if ISAS.EQ.1 then the SAS source term will be used and if ISAS.EQ.0 then the standard SST will be run.

  • Working array W10 is $\mid \nabla k \mid^{2}$

  • Working array W11 is $\mid \nabla \omega \mid^{2}$

  • Working array W11 is max (W10/$k^{2}$),W11/$\omega^{2}$)

The above operation frees up W10 working array for the following calculations

  • Strain invariant is $\sqrt{S2KW}$

  • Calculate the laplacian of U in part 7 of turkw.F

  • include IF statement for ISAS

  • Take VISCCFA and ITRGRP to calculate the laplacian, W2

  • Repeat for U, V and W

  • The work arrays for ITRGRP are W3,W4,W5,W6,W7,W8

  • U, W9 = -divgrad U
  • V, W9 = -divgrad V
  • W, W9 = divgrad W

  • W10 is used for the square root of the sum of the gradients.

Source terms

  • Calculate $L_{vk}^{min}$.

  • Calculate $L_{vk}$, and then setup max statement

  • Calculate $L$

  • Calculate $Q_{SAS}$

  • Divide working array W10 by the volume

  • Add an if statement to the $\omega$ source terms, where if ISAS.Eq.1 the source term has QSAS added to it


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

  • Change call to turbkw, 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


  • set default value, ISAS = 0

  • include incsas.h

  • include default values for $C_{SAS}$ and $\zeta_{2}$


  • ISAS = 0
  • $C_{SAS}$ = 0.11
  • $\zeta_{2}$ = 3.51
  • include incsas.h


  • include incsas.h
  • Include printout for ISAS
  • include printout for $C_{SAS}$


  • include incsas.h
  • include an IF statement to check that DDES and SAS are not both running.

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pdfpdf csas_sst_32.pdf manage 151.2 K 2011-06-19 - 22:17 NeilAshton csas calibration for the SST-SAS model
Topic revision: r1 - 2011-06-19 - 22:17:31 - NeilAshton
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22 Mar 2019


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