Thermal PDE in cylindrical coordinates at the origin

Hi,

I have a problem with a thermal PDE in cylindrical coordinates. I followed the example in Heat Distribution in Circular Cylindrical Rod .

The script runs without errors, however the solution has peculiar spot at z = 0, r = 0 where the Temperature is constantly zero. The heat source at that spot is well larger than zero and all around the spot a temperature which is as expected is reached.

I tried changing several of the pde SolverOptions or choose the mesh differently, however nothing of what I tried was successful.

Does anybody have an idea what I can do to fix this issue?

Thanks in advance

Answer 1

[Tobias]

My error was in not transforming the boundary condition correctly. I had assumed that the BC in the example just had a curios form, but the *region.y originated from the transfer to cylindrical coordinates.

With the correct BC the solution makes sense on the whole domain.

Answer 2

[Svetlana Pease]

Hi Tobias,

Are you talking about the steady-state or transient solution? The only zero temperature I get is for the transient solution at t = 0 (time step is 1 for t = 0).

Regards,

Svetlana Pease

MathWorks Documentation Group

[Tobias]

I am looking into the transient solution. Probably an issue is that my body has only ~1e-3 m in extension.

[Svetlana Pease]

In this case, you might want to use a much finer mesh. The example uses a maximum mesh edge length Hmax = 0.1. You can try using a default setting by not specifying Hmax (this will let the mesh generator guess the appropriate Hmax for your geometry) or specify a much smaller value for Hmax.

Hope this helps!

Svetlana

[Tobias]

I already had Hmax at 1e-4 which however did not help. Smaller Hmax made my PC run out of memory.

What helped a bit was however a rescaling of the whole problem by multiplying all lengths by 1000. I should also be able to achieve this by setting some absolute solverOptions but I have not looked into it yet.

[Tobias]

Is there a possibility to create the mesh with two different Hmax? I naively tried to assembly the mesh in two steps but I was not allowed to change the read-only FEMesh.

If I calculate my problem in full 3d the problem does not appear (however I cannot choose my grid fine enough to get rid of other oscillations)

[Torsten]

I'd simply start with the geometry at r = eps instead of r = 0 for eps being a small value.

Answer 3

[Svetlana Pease]

Hi Tobias,

No, there is no option to have two or more Hmax settings for the same geometry/mesh.

Regards,

Svetlana