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Laplacian DReff

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Old   October 1, 2018, 10:16
Default Laplacian DReff
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Dear FOAMers,

I hope someone can help me:

As I read in the source code of the SSG turbulence model, the diffusion coefficients of \epsilon and \bf{R} are constructed as symmetrical tensors:
template<class BasicTurbulenceModel>
tmp<volSymmTensorField> SSG<BasicTurbulenceModel>::DREff() const
     return tmp<volSymmTensorField>
         new volSymmTensorField
             (Cs_*(this->k_/this->epsilon_))*this->R_ + I*this->nu()
Now I'm wondering, how can the laplacian

fvm::laplacian(alpha*rho*DREff(), R)
be denoted in mathematical form. I had a look at the code but did not find a clear answer of how OpenFOAM produces it. In specific, I am trying to find out, in what kind of product the 2x2 diffusion matrix \bf{\Gamma}=\Gamma_{ij} and the 3x3 'Reynolds stress gradient' \nabla \bf{R}=r_{ijk} are coupled.

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