Very short heating: Heat solver artifact?

[mzenker]

Hi,

I want to examine material heating with very short (µs) heat pulses. I have set up a simple axisymmetric case and observe a strange behaviour: The temperature under the surface where the heat flow is induced is decreasing while the heat flow is switched on. I cannot think of a physical effect explaning that, so I suspect a simulation artifact. What do I do wrong? My case is in the attachment.

Thanks for a hint,
Matthias

Edit: Attachment updated. In the initial one the files might be inconsistent.

[kevinarden]

My experience with that condition is a mesh that is too coarse.

[raback]

Hi Matthias,

I think your observation is real. There exists both min and max timesteps that leads to physically sound solution. See for example paper "Minimum time‐step size for diffusion problem in FEM analysis" (cannot access it myself now...).

-Peter

[kevinarden]

time.png

(72.17 KiB) Not downloaded yet

that sudden drop to 20 (initial condition) does seem odd. Do not think that is mesh related.

I cut the time step size in half.

[kevinarden]

I changed time stepping to this and obtain a completely different result

Timestep intervals = 100
Timestep Sizes = .5e-6

time2.png

(56.37 KiB) Not downloaded yet

[mzenker]

Thanx for your replies. So at least I have not made a very trivial error.
I didn't buy the paper indicated by Peter yet.

So if I understand correctly, very small timesteps might be a problem.
Is that due to something like the internal accuracy of the solver, or is it a more fundamental effect?
Are there generally known rules how to derive the minimum timestep for a given problem?
Are there any "tricks of the trade" I could use to overcome that limitation?
Would it help to do some upscaling - e.g. use microseconds as the time scale (I would have to convert all time-related parameters including material properties)...?

Matthias

[kevinarden]

I do not think it is a real world physical problem. If you add heat it should steadily rise in temperature, if you remove heat it should steadily decrease in temperature, otherwise I do not know where the energy would be going.

It may be a mathmatical solution, integration problem. In general finer meshes and smaller time steps lead to better solutions.

Larger time steps would mean you are just skipping over the solution anomolies.

[raback]

Hi Matthias,

I do remember reading before of a discretization issue that causes problems with too small timesteps for heat equation. Could not quickly find a free reference for that. Intuitively, I can see that if the initial conditions are such that heat flux is zero that getting the desired heat flux instantaneously could be a challenge.

Personally, if possible, I try to use Robin BCs rather than Neumann. I.e. define "heat transfer coefficient" and "external temperature". Then I think this problem does not exist.

-Peter

[mzenker]

Hi,

in fact this case was intended to be a pre-study. In my "real" case, the heating is done by a current through Joule heating. So I have very short current pulses (of the order of 3 us, repeated e.g. every 50 us) and want to examine the heating of the material.
I have run the case with the static current solver as heat source and did not observe that kind of problem so far. I am just struggling with edge effects leading to (unphysically?) high current densities at the borders of the area where the current enters the material. But that is another story...
But still the phenomenon of decreasing temperature is surprising...

Thank you for your help,

Matthias