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.