[Kellis]

Hello all,

I am attempting to solve a conjugate heat transfer problem where viscous heating plays an important role in the overall process. I am solving the energy equation as follows:



Due to the nature of the problem, the viscous heating term varies many orders of magnitude over the width of a few cells, and causes some instabilities / oscillations when solving for the temperature. To combat this, I am hoping to implement some sort of smoothing algorithm which conserves the overall amount of viscous heating, but distributes it within a wider area to make the computation more stable. For instance in 1D, assuming a uniform grid spacing, this smoothing algorithm might turn a field that looks like this:

[ 1 1 1 10 1 1 1 ]

Into one which looks like this:

[ 1 2 3 4 3 2 1 ]

Ideally, the "width" of the spread would be controllable by the user. I am sure such an algorithm exists already, but I am not sure what the correct search terms would be, and my initial efforts to find such a method have not yielded any good leads.

If anyone has a suggestion for a method I might try, I would be grateful. Additionally, any other strategies I might try to increase the stability of the problem would be appreciated.

Thanks,
Kellis

[mAlletto]

Hello,

You can try to first interpolate to the faces and then avarage over the faces of the cell. The code would look like this:

volScalarField smoothedSoure (fvc::average(fvc::interpolate(source)));

This will smooth the source a bit

[mkraposhin]

You can solve diffusion equation in pseudo-time, like that:




dimensionedScalar pseudoDeltaT ("dT", dimTime, 1.0);
dimensionedScalar Dphi ("Dphi", dimLength*dimLength/dimTime, 1.0);



solve
(
fvm::Sp(1.0/pseudoDeltaT, Phi)
- fvc::Sp(1.0/pseudoDeltaT, Phi)
- fvm::laplacian(Dphi, Phi)



);

[mAlletto]

What's the purpose of

fvm::Sp(1.0/pseudoDeltaT, Phi)
- fvc::Sp(1.0/pseudoDeltaT, Phi)

Numerical stability of the equations?

[mkraposhin]

Originally Posted by mAlletto

What's the purpose of

fvm::Sp(1.0/pseudoDeltaT, Phi)
- fvc::Sp(1.0/pseudoDeltaT, Phi)

Numerical stability of the equations?

If you use diffusion equation w/o temporal term, then your Phi distribution will be smoothed across a whole domain. But with adjustment of ratio between "pseudoDeltaT" and Dphi you can tune how many cells around initial field will be affected during one pseudo iteration.

[mAlletto]

That's interesting. Can you recommend someone regarding about the method?

[mkraposhin]

This is a simple idea, which arises from the concept of numerical diffusion of convection equation.


http://www.mathematik.tu-dortmund.de.../Transport.pdf


Or just walk around this personal page: http://www.mathematik.tu-dortmund.de/~kuzmin/

[joshwilliams]

Originally Posted by mAlletto

That's interesting. Can you recommend someone regarding about the method?

I used code from the CFDEMcoupling library to do something similar. You can copy the function from this GitHub repository. There are some user-defined lengths and lower/upper limits you can use to tune the diffusion.