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Disagreement between total heat flux and lagrange multiplier

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Hi all,

I am modeling a two-phase Stefan problem (melting) and come to notice that the total flux across the phase transition boundary is different both in magnitude and, at somee point, opposite in direction (net flux I suppose? see attached "Lagrange vs total heat flux"). This results in the immediate sodification of the liquid domain which, according to the analytical solution, supposedly grows in size. I found little documentation regarding the exact representation of lagrange multiplier other than it being heat flux in heat transfer module, so I have had a hard time locating the real issue.

My model is an adaptation of the tin melting example.

It seems to me that lagrange multiplier (thermal) does account for the heat fluxes from both directions across an internal boundary, so what could explain the disparity? How should I remedy it?

I uploaded two snapshots of the plots. In "Lagrange vs total heat flux", the green line represents the total heat flux curve while the blue one represents the lagrange multiplier. The hump/cavity later in time is the result of viscous dissipation from a shear driven wall in the liquid domain. In "initial temp profile", where the first space derivative is not continuous ~0.0005m is where I defined my initial position of the phase transition boundary.



1 Reply Last Post 18 giu 2020, 11:18 GMT-4

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Posted: 4 years ago 18 giu 2020, 11:18 GMT-4

Hi,

I am not sure how to best help you, but when I was trying to understand Lagrange multipliers in COMSOL, I found this webpage to be incredibly useful : http://www.softeng.rl.ac.uk/st/projects/felib3/Docs/html/Intro/intro-node68.html

Once you understand it, the little pieces of info scattered about Lagrange multipliers in the knowledge base and the comsol blog, start to make a lot more sense. :)

Sometimes the flux computed by taking derivatives can differ from the Lagrange multiplier simply because your mesh is too coarse. I am not optimistic that this is indeed what is happening here, but it's worth doubling the number of mesh points and see if that changes your second plot.

Hi, I am not sure how to best help you, but when I was trying to understand Lagrange multipliers in COMSOL, I found this webpage to be incredibly useful : http://www.softeng.rl.ac.uk/st/projects/felib3/Docs/html/Intro/intro-node68.html Once you understand it, the little pieces of info scattered about Lagrange multipliers in the knowledge base and the comsol blog, start to make a lot more sense. :) Sometimes the flux computed by taking derivatives can differ from the Lagrange multiplier simply because your mesh is too coarse. I am not optimistic that this is indeed what is happening here, but it's worth doubling the number of mesh points and see if that changes your second plot.

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