[xuegy]

Hello all,

I have a mass transport equation with term
CodeCogsEqn.png
where c is unknown concentration to be solved and T is known temperature from previous equation.
I transformed the above term into
CodeCogsEqn (2).png
And since term grad(T) is dominating, I want to solve grad(C) implicitly. However there's only fvc::grad(C) to use.

So is there any possibility to solve this term implicitly?

Thanks.

[Tobi]

No, the gradient can only be calculated with the last stored values. I never heard that people calculate the gradient implicitly. Now I am wondering, if it would be possible in general. Well. In FOAM it is not possible. See page 35: http://foam.sourceforge.net/docs/Gui...mmersGuide.pdf

[xuegy]

Actually I don't need an implicit gradient. All I need is an implicit inner product of two gradients, which is a scalar.
Or, can I discretize the original term directly?

[Tobi]

Hi, the First Term is a laplacian which can be treated implicitly.

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[Tobi]

Hi,

I was talking to my colleague Chris about that and I am sorry to get the message wrong.
You are solving for c which I was not aware yesterday. So what you could try is:

a) Solve TEqn.

b) Build you gradT = fvc::grad(T) field

c) Solve your equation and treat your divergence term implicitly like:



which would be:

fvm::div(gradT, c)

[xuegy]

No, this won't work.
It says:

cannot convert ‘gradT’ (type ‘Foam::volVectorField {aka Foam::GeometricField<Foam::Vector<double>, Foam::fvPatchField, Foam::volMesh>}’) to type ‘const surfaceScalarField& {aka const Foam::GeometricField<double, Foam::fvsPatchField, Foam::surfaceMesh>&}’

That's why I split the divergence term.

[Tobi]

Ah, of course. I am sorry again. So you have to interpolate the gradient to the surface first. Thus you have to do the following:

a) create a new surfaceScalarField

b) Interpolate the gradT to the surfaces

c) use this field in the divergence term

Like:

volScalarField gradT = fvc::grad(T);

surfaceScalarField gradTf = fvc::interpolate(gradT) & mesh.Sf();

fvm::div(gradTf, c)

[xuegy]

Yeah I can compile it. I can't wait to see the result of a testing case.

So is it something like a heat flux without thermal conductivity?

[Tobi]

Yes, the physical meaning of the divergence is the flux which is going in and out of an volume element. I have no idea how you got to that term because it would mean that the concentration (of some species?), is transported by the temperature gradient (like a temperature flux). Thus, the concentration is moving to the highest temperature (if I have the sign correct - or vice versa). However, normally only the velocity can transport a quantity by fluxes. But maybe there is some physical meaning behind your term that I don't know. In the general conservation equations, I never saw a term like that.

But nice to hear, that it is working.

[xuegy]

It's called thermophoresis. Particles can be driven by temperature gradient.