What does fvm::laplacianCorrection do?

agustinvo · March 7, 2024, 06:52

Hi,

I am implementing new turbulence thermophysical transport models in OpenFOAM 11, and I am dealing with the divq function:

Code:

template<class TurbulenceThermophysicalTransportModel>
tmp<fvScalarMatrix>
eddyDiffusivity<TurbulenceThermophysicalTransportModel>::divq
(
    volScalarField& he
) const
{
    // Return heat flux source as an implicit energy correction
    // to the temperature gradient flux
    return
        -fvc::laplacian(this->alpha()*this->kappaEff(), this->thermo().T())
        -fvm::laplacianCorrection(this->alpha()*this->alphaEff(), he);
}

where the fvm::laplacianCorrection appears. According to the corresponding commit:

Quote:

Now that thermal transport is implemented as an energy implicit correction on an explicit temperature gradient formulation it is more efficient if the implicit correction contains only the implicit terms of the matrix and not the explicit non-orthogonal or anisotropic correction terms which are cancelled anyway when the evaluation of the matrix for the current state is subtracted. The new fvm::laplacianCorrection functions provide a convenient mechanism to efficiently evaluate only the implicit correction to the laplacian and is now used in all the thermophysicalTransportModels.

but it is not so clear to me this description.

What I understand when I see the function is that I add the divergence of the effective heat flux in terms of the temperature gradient

$\nabla \cdot q_{eff} = -\nabla\cdot \left(\kappa_{eff} \nabla T\right)$

and I do some kind of correction on the energy, which is the equation's variable. In this case, considering on one phase the extra term is:

$-\nabla\cdot \left(\alpha_{eff} \nabla h\right) \equiv -\nabla\cdot \left[\frac{\kappa_{eff}}{C_p} \nabla \left(C_p T \right)\right]$

which has some simmilarities to the previous equation.

My question is: what is actually doing in this case? I am planning to add anisotropic diffusivity models like
$q_{turb, i} = - C_{\theta} R_{ij} \frac{\partial T}{\partial x_j}$
but do not undestand how can I benefit from this laplacianCorrection function.