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# Eddy viscosity of smagorinsky LES model

Posted by swang251
 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)[1] or the one by Krafczyk 2003[2]. 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

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