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r=0 singularity in using axisymmetric PDE mode
Posted 2012年6月10日 GMT-4 11:45 Modeling Tools & Definitions, Parameters, Variables, & Functions 1 Reply
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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?
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 2012年6月10日 GMT-4 17:19
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Posted:
1 decade ago
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
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