Implementing Radiative Losses in Thermal Model

[pushkar...@gmail.com]

Dear deal.II Community

I would like to seek help regarding the implementation of radiative losses in thermal model as a BC which will make the system non linear. So it would be much helpful if someone could direct to relevant tutorial program implementing the above BC.

Regards

Pushkar 

[Wolfgang Bangerth]

On 6/3/21 7:10 AM, pushkar...@gmail.com wrote:
>
> I would like to seek help regarding the implementation of radiative losses in
> thermal model as a BC which will make the system non linear. So it would be
> much helpful if someone could direct to relevant tutorial program implementing
> the above BC.

Pushkar,
these sorts of nonlinear boundary conditions are generally included into the
weak formulation of the problem via Neumann boundary conditions. Your weak
formulation then becomes nonlinear, and if you take a look at step-15, you
will see how this kind of problem should be solved.

(You could also look at the new step-72 and step-77 programs to see how
certain aspects of this could be simplified.)

Best
Wolfgang


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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[blais...@gmail.com]

In addition to what Wolfgang said.

If you want to add radiation boundary condition, the first step would be to implement a general robin condition. You can see radiation BC following Stefan law as a non-linear Robin BCs. Once you have a non-linear heat equation solver ready that works with Robin BCs, you can just make your Robin boundary condition non-linear and the rest will follow. Luckly, the Jacobian matrix arising from the radiation BC is simple because it a  polynomial BC.

Good luck  and don't hesitate to ask more questions :)
Best

Bruno

[Pushkar Pandit]

Thanks alot for directing me to the appropriate tutorials as well as suggestion to start off with generalized Robin BC and will seek guidance further as well .

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