'fourth' snGrad Scheme

Functionality to add/problem to solve

Fourth-order snGrad scheme with non-orthogonal correction.

Target audience

Fourth order gradient can be used in the removal of field decoupling.

Currently the workaround for the Laplacian of a vector is:

1. Create a volTensorField using fourth grad scheme.
2. Apply Gauss linear div scheme to evaluate its laplacian.

The extra step can be avoided if fourth snGrad scheme is available.

Proposal

For some reason it's available in the official user's guide but not implemented in both .com and .org version. The code is already available in foam-extend: https://sourceforge.net/p/foam-extend/foam-extend-4.1/ci/nextRelease/tree/src/finiteVolume/finiteVolume/snGradSchemes/fourthSnGrad/ so should be easy to add.

What does success look like, and how can we measure that?

Applying Laplacian with 4th order snGrad directly like:

Gauss linear fourth;

The below screenshot is a 2D viscoelastic flow benchmark case Left: fourth gradient then Gauss linear divergence workaround . Right: Gauss linear corrected laplacian scheme.

Links / references

The paper below is a direct application of the fourth order scheme:(they use foam-extend in their paper)

https://www.sciencedirect.com/science/article/pii/S0045793018300045

A stable numerical implementation of integral viscoelastic models in the OpenFOAM® computational library, Araújo et al. 2018

Funding