Interpolation scheme for electric current / heat flux

assigned to @Sergio

Discussed quickly with @andy - is this much different than src/finiteVolume/interpolation/surfaceInterpolation/schemes/harmonic/harmonic.H ?

I denote by phi_1 the potential in cell 1, phi_2 in cell 2, and phi_f the potential at the face between both cells. Similarly, delta_1 means the distance from cell centre 1 to the face, delta_2 the distance of cell 2 to the face, and delta the distance between both cell centres.

Harmonic interpolation is then

\varphi_f = \frac{1}{\frac{\delta_1/\delta}{\varphi_1}+\frac{\delta_2/\delta}{\varphi_2}}.

However, the missing interpolation scheme is

\varphi_f = f\cdot\varphi_1 + (1-f)\cdot\varphi_2

with

f = \frac{\delta_2\sigma_1}{\delta_1\sigma_2 + \delta_2\sigma_1}.

So yes, both schemes are different. The new schemes accounts for the change of electric conductivity, while harmonic interpolation does not.

By Norbert Weber on 2019-07-31T11:36:58 (imported from GitLab project)

## Reattaching the author to the issue ticket: @dl6tud ##

Hi Norbert,

Is not the harmonic mean the exact solution for the heat flux?. Which is the name of your mean?.

Thanks

Sergio

Hello Sergio,

the harmonic interpolation is perfect for computing the thermal CONDUCTIVITY at the wall:

laplacianSchemes
{
    laplacian(lambda,T)         Gauss harmonic uncorrected;
}

However, a new scheme is necessary for computing TEMPERATURE at the face:

gradSchemes
{
    grad(T)     Gauss volWeighted "lambda";
}

This scheme reads the thermal conductivity from the object registry ("lambda"). Then, it weights the temperature of neighboring cells using the thermal conductivity to get the temperature on the face.

By Norbert Weber on 2019-08-01T15:38:54 (imported from GitLab project)

Hi Norbert,

OK. I see your point. We need a correct name for this weighted interpolation. We have a "weighted" interpolation already. Do you know the name of this interpolation? If you provide the code, we can included. Thanks Sergio

I discussed with the colleagues. It is not easy to find a good name for the scheme. The words "weighted" and "flux" (referring to e.g. heatflux) fit well. "Conductivity" does not fit well, because the scheme might be used for diffusivities, as well. Might "weightedFlux" be an option?

By Norbert Weber on 2019-08-07T14:52:14 (imported from GitLab project)

A suggestion for the name:

the scheme you are talking about is required to correctly deal with problems where the field which multiplies the gradient is discontinuous across the face. Otherwise, if this field changes continuously in the domain, the standard linear interpolation would be more appropriate.

Therefore, I’d look for a name which highlights this.

There are also other applications where this scheme can be potentially employed, for example the discretisation of the product 1/rho*grad(p) in the momentum equation when the cell face overlaps with the interface between two fluid phases (see [1]).

[1] Vukčević, V., Jasak, H., Gatin, I., 2017. Implementation of the ghost fluid method for free surface flows in polyhedral finite volume framework. Comput. Fluids 153, 1–19.

By Luca Cornolti on 2019-08-08T12:22:38 (imported from GitLab project)

It seems to me that this interpolation scheme is useful for getting fluxes in general such as (flux = K grad(T)), then Tf is needed weighted with K being included. Although the expression fvc::grad(T), k is not specified. It looks like weightedFlux could be an option.

I agree with both of you. For me, "weightedFlux" would be fine. If you agree, I will push the feature at the beginning of September, as I am on holidays for the next two weeks.

By Norbert Weber on 2019-08-09T11:51:38 (imported from GitLab project)

Hi Norbert (@dl6tud),

@andy is back tomorrow and can give guidance. The short upshot (Fazit) as I know it -we have limited branching/pushing with our community edition of gitlab. But wait for a more definitive answer from @andy.

Ciao, /mark

Dear Norbet, On which branch are you trying to push? Can you send me the code to review and I could add it to our development branch Thanks

Dear Sergio,

starting from the development branch, I created a new feature branch and tried to push that (did not work). Please find the code attached to this post. I read the code styling guide, and hope to have respected everything. If I did something wrong, I would be happy for feedback. Thank you!

weightedFluxInterpolationScheme.zip

By Norbert Weber on 2019-09-04T10:25:32 (imported from GitLab project)

Dear Norbert, Thanks for the code. It looks good. Still need to check how we want to implement this variation of grad. I think this should look like: fvc::grad(sigma, T) similar as for the fvc::laplacian(kappa, T).

q = sigma*fvc::grad(T), this implies the flux-weighted interpolation of sigma for to get an accurate q, and the user needs to know that the scheme used to interpolate grad(T) uses sigma.

But, ideally we'd want i.e q = fvc::grad(sigma, T), where sigma is already in the expression. where sigma could be a face, cell centre or scalar values or tmp's of those. This requires more coding as the options are larger.

Thanks

Sergio

Hi Norbert, I am pushing the code for the new version, I hope. Do you have a simple test case where it can be shown the benefits of this scheme for fluxes? Thanks Sergio

Thank you! Sorry for the silence - I was on holidays. I do have indeed a test case. Should it be for you only, or to push it with the new openfoam version?

By Norbert Weber on 2019-09-28T15:51:27 (imported from GitLab project)

I build a new branch with some other numeric. Let me know how you want your contribution in the header file. If you please can send me a small tutorial case which I can add to our tutorial cases. Before making the release we need to follow some code review internally. We'll try to make for this release. Thanks

Dear Sergio, for the best (=simplest) tutorial case I would need laplacianFoam. Unfortunately, laplacianFoam solves fvm::laplacian(DT, T) with DT being a dimensionedScalar - but I would need DT as a volScalarField. Might we change laplacianFoam such that it reads DT with READ_IF_PRESENT as volScalarField?

It would be good for me if my name, and a reference to the article appears in the header file. Thank you!

By Norbert Weber on 2019-10-03T08:05:00 (imported from GitLab project)

Yes, I agree. When you have it ready send it over and I consult if we will make DT a volScalarField instead of dimensionedScalar. Thanks

I'd need an affilation for the header:

Copyright (C) YEAR AUTHOR,AFFILIATION

The reference goes bellow.

Thanks

Please find the testcase here: testcase.zip. It computes the heat flow in a 1D bar, and illustrates the difference of both laplacian(DT,T) Gauss linear corrected and laplacian(DT,T) Gauss harmonic corrected, and grad(T) Gauss linear and grad(T) Gauss weightedFlux "DT". Gnuplot is used to show the results.

I modified in laplacianFoam in createFields.H:

dimensionedScalar DTscalar(transportProperties.lookupOrDefault<dimensionedScalar>("DT",0.0));

volScalarField DT
(
    IOobject
    (
        "DT",
        runTime.timeName(),
        mesh,
        IOobject::READ_IF_PRESENT,
        IOobject::AUTO_WRITE
    ),
    mesh,
    DTscalar
);

volVectorField q
(
    IOobject
    (
        "q",
        runTime.timeName(),
        mesh,
        IOobject::NO_READ,
        IOobject::AUTO_WRITE
    ),
    mesh,
    dimensionedVector("q", dimensionSet(0,1,-1,1,0,0,0),vector::zero)
);

and in laplacianFoam.C: q = DT*fvc::grad(T);

Thank you!!!

By Norbert Weber on 2019-10-05T09:28:54 (imported from GitLab project)

Hi Norbert, Thanks for the tutorial. I modified laplacianfoam accordingly. This is the heat flux graphs I've got:

Is this correct?.

Thanks

Sergio

Hi, My mistake, now I can see the flux doing the correct interpolation Thanks

Perfect! Thanks a lot!

By Norbert Weber on 2019-10-07T19:26:48 (imported from GitLab project)

changed the description

mentioned in commit 01b4519f

mentioned in commit d04de0d4

mentioned in commit 3b6ba059

Resolved in v1912 release

closed

Interpolation scheme for electric current / heat flux

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Interpolation scheme for electric current / heat flux

Functionality to add/problem to solve

Target audience

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

Links / references

Funding

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