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# Eddy viscosity of smagorinsky LES model

 Eddy viscosity of smagorinsky LES model February 27, 2018 06:28AM Registered: 1 year ago Posts: 6
Hi,

I am trying to understand static Smagorinsky model implemented in Palabos. As described in the documentation:
Quote
In the Palabos implementation, the strain-rate is computed from the stress tensor \Pi.
I could understand this from the relationship between the stress tensor and strain rate: Pineq=-2cs2*rho*tau*S.

However, when I look at the file /complexDynamics/smagorinskyDynamics.hh: , I could not understand how the function computeOmega calculates the omega_{total} where the code is
```Language: C++static T computeOmega(T omega0, T preFactor, T rhoBar, Array<T,SymmetricTensor<T,Descriptor>::n> const& PiNeq)
{
T PiNeqNormSqr = SymmetricTensor<T,Descriptor>::tensorNormSqr(PiNeq);
T PiNeqNorm    = std::sqrt(PiNeqNormSqr);
T alpha        = preFactor * Descriptor<T>::invRho(rhoBar);
T linearTerm   = alpha*PiNeqNorm;
T squareTerm   = (T)2*alpha*alpha*PiNeqNormSqr;
// In the following formula, the square-root appearing in the explicit form of
//   omega is developed to second-order.
return omega0*(1-linearTerm+squareTerm);
}```
.

This calculation seems to be a different form compared to the one in the paper by Hou, et al. (1994) or the one by Krafczyk 2003. If so, what is the benefits of this form?

Could anyone help explain this or provide any reference?

Thank you in advance.

With best,
Song

 Hou, et al. 1994, "A lattice Boltzmann subgrid model for high Reynolds number flows"
 Krafczyk 2003 "LARGE-EDDY SIMULATIONS WITH A MULTIPLE-RELAXATION-TIME LBE MODEL"
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