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r=0 singularity in using axisymmetric PDE mode

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I understand in pde mode nabla operator differs that in other modules for 2D axisymmetry. When I try to model diffusion in general PDE/coefficient PDE/classical PDE, COMSOL cannot handle the singularity at r =0 very well:
d(p,t)+d(d(p,r),r)+d(d(p,z),z)==-1/r*d(p,r)
r*d(p,t)+d(r*d(p,r),r)++d(r*d(p,z),z)==0
both fail.
I wonder what to do?

1 Reply Last Post 10 giu 2012, 17:19 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 10 giu 2012, 17:19 GMT-4
Hi

there are several mathematical ways to avoid a singularity when intrgrating over a domain, either we integrate around it, but without going "onto" the singularity, or we remove the singularity by an appropriate variable change, then the inverse is applied to the results.

I assume that in PDE mode, nothing is done specifically, leaving the user choose his method. While for all or most physics 2D-axi, COMSOL has implemented these different mathematical means to get around the r=0 singularity.

Astoday I'm doing engineering developments, I trust COSMOL, and the scientists using it, that the 2D-axi mathematical formulation has been handled correctly. But certainly, if I had ben working on my PhD with COMSOL, I would have added a chapter on these methods to show I understand them and to prove they are correct.

I suppose one can get some good clues what is being done by analysing the physics equation view, and comparing to the PDE math equations view

--
Good luck
Ivar
Hi there are several mathematical ways to avoid a singularity when intrgrating over a domain, either we integrate around it, but without going "onto" the singularity, or we remove the singularity by an appropriate variable change, then the inverse is applied to the results. I assume that in PDE mode, nothing is done specifically, leaving the user choose his method. While for all or most physics 2D-axi, COMSOL has implemented these different mathematical means to get around the r=0 singularity. Astoday I'm doing engineering developments, I trust COSMOL, and the scientists using it, that the 2D-axi mathematical formulation has been handled correctly. But certainly, if I had ben working on my PhD with COMSOL, I would have added a chapter on these methods to show I understand them and to prove they are correct. I suppose one can get some good clues what is being done by analysing the physics equation view, and comparing to the PDE math equations view -- Good luck Ivar

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