Interpolation scheme for electric current / heat flux

Functionality to add/problem to solve

An electric current is calculated as

J = \sigma\cdot\nabla\varphi.

The gradient of the electric potential can not be calculated using the Gauss theorem with LINEAR interpolation of the potential . A special interpolation scheme is necessary. As described below, the potential at the face needs to be weighted by the conductivity of both cells.

Target audience

The mentioned interpolation scheme is necessary for computing the gradient of

• electric potential (i.e. electric current)
• temperature (i.e. heat flux)

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

I use the mentioned interpolation scheme for several years. It is already validated and published.

Links / references

Weber, N.; Beckstein, P.; Galindo, V.; Starace, M.; Weier, T.: Electro-vortex flow simulation using coupled meshes, Computers and Fluids 168(2018) 101-109

It is Eqn. 16/17 in the Arxiv version.

Funding

I can provide the source code.

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