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Units of Lagrange multipliers

Posted Apr 14, 2011, 7:00 a.m. EDT Chemical Reaction Engineering, Parameters, Variables, & Functions Version 4.1 3 Replies

David964
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COMSOL has a very nice interface for units and dimensional analysis, but they forgot to define the units of the Lagrange multiplier variables! For example, I have a 2D chemical convection-diffusion equation in COMSOL 4.1, and a boundary condition with a fixed concentration. I set it to the weak form, and then there's a Lagrange multiplier variable that should represent flux of the chemical through the boundary.

The problem is, the Lagrange multiplier variable has no units in the program! It's treated as a dimensionless variable. But flux obviously does have units. Am I confused, or is this is an error in the program?

I am guessing that my lagrange multiplier value is the value in the SI units: in (moles per m^2 per second). But I want to be 100% sure. Can anyone confirm that they checked this?

Thanks in advance!
3 Replies Last Post Apr 14, 2011, 9:39 p.m. EDT
Kai Herbrig
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Posted: 1 decade ago Apr 14, 2011, 9:08 a.m. EDT
Hi,

these multipliers should have SI units.

But you can check it on your own model: compare these values with 'normal total flux'. Ideally they should be equal, but of course they aren't, since they are calculated in different ways. But they never differ very much (the constraints are more precise). 'normal total flux' has units. Now you can compare the values and et voilá you know which units your constraints have.
Hi, these multipliers should have SI units. But you can check it on your own model: compare these values with 'normal total flux'. Ideally they should be equal, but of course they aren't, since they are calculated in different ways. But they never differ very much (the constraints are more precise). 'normal total flux' has units. Now you can compare the values and et voilá you know which units your constraints have.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Apr 14, 2011, 11:17 a.m. EDT
Hi

I got back the message fro support that it will come in next release ;)

everything was not implemented in v4.1.

But it's summarized somewhere in the doc, in a table for the different physics i.e. [Pa] for solids

--
Good luck
Ivar
Hi I got back the message fro support that it will come in next release ;) everything was not implemented in v4.1. But it's summarized somewhere in the doc, in a table for the different physics i.e. [Pa] for solids -- Good luck Ivar
David964
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Posted: 1 decade ago Apr 14, 2011, 9:39 p.m. EDT
Thanks! I followed Kai's advice and compared to the normal-total-flux variable. It was indeed SI -- mole/m^2/second.

To fix all the other problems -- like errors in formulas and wrong unit-labels on graphs -- I defined a new variable ("conc_lm_with_units"), defined as the original lagrange multiplier ("conc_lm"), multiplied by its unit ("1[mol/(m^2*s)]"). Then I use conc_lm_with_units in all my equations and never use conc_lm.

So I'm all set now, thanks again.
Thanks! I followed Kai's advice and compared to the normal-total-flux variable. It was indeed SI -- mole/m^2/second. To fix all the other problems -- like errors in formulas and wrong unit-labels on graphs -- I defined a new variable ("conc_lm_with_units"), defined as the original lagrange multiplier ("conc_lm"), multiplied by its unit ("1[mol/(m^2*s)]"). Then I use conc_lm_with_units in all my equations and never use conc_lm. So I'm all set now, thanks again.

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