Temperature osscilations for low thermal diffusivity materials

[Muhammad Mashhood]

Dear users,

                I am working with deal.ii step-26 to implement temperature dependent thermal diffusivity. Currently for thermal diffusivity values > order of 1e-2 the results are quit satisfactory but if I use the low thermal diffusivity values like the order of 1e-6 to 1e-3, I get temperature oscillations (temperature going to -ve value even with all positive temperature initial and boundary conditions in domain and at boundaries).

If anyone has faced the same issue in thermal conduction simulations or knows the criteria to keep simulation stable in terms of thermal diffusivity, time step and mesh size then kindly suggest and share the opinion. Thank you in advance!

Regards,

Mashhood

[Wolfgang Bangerth]

In the limit of no thermal diffusivity, your equation ends up as an ordinary
differential equation and that means that you lose stability in the H^1 norm
-- in other words, you will get oscillations. That's just part of the nature
of the equation.

What is the situation you are trying to model that leads to such a small
diffusivity?

Best
W.


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

[Chinedu Nwaigwe]

Wolfang is right.  Negligible values of diffusion or thermal coefficients lead to a compete change in the physics of the problem.  In that case if there are source terms the solution might become negative and if there is no source it will become steady. Things might get worse if advection term is involved. 

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[Muhammad Mashhood]

Hi Prof. Wolfgang! Thank you for the response. Indeed the solution is quite reasonable and validated with analytical solution if diffusivity is kept bigger.

Actually in my case I am using the metals and metallic alloys where the thermal diffusivity are of the range of 1e-5 to 1e-4 m^2/s (I wonder there might be an alternative way to simulate with these physical properties values).

Just as a further explanation, the approach to vary the diffusivity is also in a way that it is calculated from U_old temperature vector and remains same for current time step.

[Muhammad Mashhood]

Thanks for sharing the observations Chinedu. So far I am keeping the source term off for a while i.e. not needed currently. I am sharing the result and description in the attachment.

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