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Difference between "Log" and "Linear" equation formulation, Plasma module

Posted Feb 28, 2013, 12:36 p.m. EST Plasma Physics 5 Replies

Peyman Dordizadeh
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Hi everyone,

I have a question which couldn't find any answer in the documents. I'm modeling positive corona discharge in plasma module. The documents of software suggest to set the "Equation formulation" as "log" which solves the model for logarithm of "electron density" and "electron energy density" rather than solving for "electron density" or "electron energy density" itself.

There's something I don't understand, The results for logarithmic formulation and linear formulation are totally different from each other. Results of linear formulation seem to be making sense compared to the real experimental data; but there's still a big problem with linear formulation which produces negative values for ions' number density.

I'm thinking about getting back to logarithmic formulation, but first I have to figure out the reason of the huge difference between linear and logarithmic results.

I do appreciate any insight or idea about this issue.
Peyman.
5 Replies Last Post Aug 5, 2015, 6:47 p.m. EDT
COMSOL Moderator

Hello Peyman Dordizadeh

Your Discussion has gone 30 days without a reply. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help.

If you do not hold an on-subscription license, you may find an answer in another Discussion or in the Knowledge Base.

Jane Ni
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Posted: 1 decade ago Oct 14, 2013, 4:18 a.m. EDT
Hi~~ have you solved your problem? I came across the same problem as yours. So I also wondering why?


Hi everyone,

I have a question which couldn't find any answer in the documents. I'm modeling positive corona discharge in plasma module. The documents of software suggest to set the "Equation formulation" as "log" which solves the model for logarithm of "electron density" and "electron energy density" rather than solving for "electron density" or "electron energy density" itself.

There's something I don't understand, The results for logarithmic formulation and linear formulation are totally different from each other. Results of linear formulation seem to be making sense compared to the real experimental data; but there's still a big problem with linear formulation which produces negative values for ions' number density.

I'm thinking about getting back to logarithmic formulation, but first I have to figure out the reason of the huge difference between linear and logarithmic results.

I do appreciate any insight or idea about this issue.
Peyman.


Hi~~ have you solved your problem? I came across the same problem as yours. So I also wondering why? [QUOTE] Hi everyone, I have a question which couldn't find any answer in the documents. I'm modeling positive corona discharge in plasma module. The documents of software suggest to set the "Equation formulation" as "log" which solves the model for logarithm of "electron density" and "electron energy density" rather than solving for "electron density" or "electron energy density" itself. There's something I don't understand, The results for logarithmic formulation and linear formulation are totally different from each other. Results of linear formulation seem to be making sense compared to the real experimental data; but there's still a big problem with linear formulation which produces negative values for ions' number density. I'm thinking about getting back to logarithmic formulation, but first I have to figure out the reason of the huge difference between linear and logarithmic results. I do appreciate any insight or idea about this issue. Peyman. [/QUOTE]
Peyman Dordizadeh
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Posted: 1 decade ago Oct 14, 2013, 11:02 a.m. EDT
Hi

Unfortunately I don't have answer for this. I totally switched to logarithmic because of those negative values in linear mode.

Regards.
Peyman.
Hi Unfortunately I don't have answer for this. I totally switched to logarithmic because of those negative values in linear mode. Regards. Peyman.
Daniel Smith COMSOL Employee

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Posted: 1 decade ago Oct 15, 2013, 10:31 a.m. EDT
Hi Peyman, for the same initial conditions, the log and linear formulations should give the same results. The log formulation is the default option because it prevents negative values for the electron density, mean electron energy and heavy species mass fractions from occurring. If you have a model which gives different results for the two formulations, please send it to support@comsol.com so we can investigate.
Hi Peyman, for the same initial conditions, the log and linear formulations should give the same results. The log formulation is the default option because it prevents negative values for the electron density, mean electron energy and heavy species mass fractions from occurring. If you have a model which gives different results for the two formulations, please send it to support@comsol.com so we can investigate.
Peyman Dordizadeh
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Posted: 10 years ago May 15, 2014, 11:06 p.m. EDT
It's been a while since I posted this topic, but I realized later that the difference between two formulations actually is the fact that the log formulation has stabilization term term which adds exponential term to the source term of the species trying to avoid approaching zero density. If you got rid of that stabilization term you'll have same results as linear formulation.
It's been a while since I posted this topic, but I realized later that the difference between two formulations actually is the fact that the log formulation has stabilization term term which adds exponential term to the source term of the species trying to avoid approaching zero density. If you got rid of that stabilization term you'll have same results as linear formulation.
Alexander Lindsay
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Posted: 9 years ago Aug 5, 2015, 6:47 p.m. EDT
Peyman (or anyone): where did you find the form of the stabilization terms that Comsol adds for the plasma model for the logarithmic formulation? I'm looking in the equation view and not finding anything.
Peyman (or anyone): where did you find the form of the stabilization terms that Comsol adds for the plasma model for the logarithmic formulation? I'm looking in the equation view and not finding anything.

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