[granzer]

Hello,
Just needed some simple clarification. From the 'Numerical Schemes' chapter (Chapter 4.5) of OpenFOAM User Guide from CFD direct, I can see that explanation for the gradient schemes says that it includes 'diffusion' type terms .

The Laplacian Scheme also of course includes the diffusion terms. So if the viscosity is not a constant in the flow equations does it mean that the viscous diffusion term will be discretized by the Divergence term? Any explanation will be helpful. Thank you.

[granzer]

Reference

[sharonyue]

The Laplacian term discretized in OpenFOAM equals to surface normal gradient multiplying magnitude of the surface. In quasi-code: fvc::laplacian(nu, U) = nuf*fvc::snGrad(U)*mesh.magSf(). Divergence term equals to summation of flux, which comes from the Gaussian theorem. In quasi-code: fvc::div(phi) = sum(phi). Therefore, we say it sounds like convection.

Indeed, for nabla cdot (nabla T), you can use both to discretize it, such as fvc::div(fvc::grad(T)), or fvc::laplacian(T), but the latter one employes the snGrad() and it further uses compact stencil (you will see one summation in math). The first one employs the extended stencil (you will see two summations in math). One important application is the usage of laplacian equation of pressure. The compact stencil can try its best to erase oscillation.

Sorry, I did not notice your last sentence. Regarding the viscosity, it simply uses interpolation scheme, e.g., central linear.