unbounded behaviour for liquid temperature in crystallization/melting cases

[Kaustubh Thakurdesai]

Hi All

I have been working on simulating melting and crystallization cases in Basilisk. For these crystallization cases, I am working on modifying the cases from ‘alimare’ sandbox. I have been able to modify the melting and crystallization simulation cases for them to be compatible with the current Basilisk version and simulate them as well with some beautiful results matching to a large extent.

However, there are certain issues, stated below that I am facing with the code and any help or guidance would be of great help.

Following are the issues:

1)    For both crystallization and melting cases, I am trying to output temperature in the domain at every time step and I observe that the temperature at the interface between two phases jumps out of bounds right in the very first iteration. For example, in the crystallization case, if the supercooled liquid temperature is -0.8 and solid is 0, I am observing values like 15 , 1200 or something like that, for the liquid boundary temperature at the interfaces, which ideally should always be between 0 and -0.8.

2)    While the simulation is getting completely run till last timestep, this appears to be a serious fundamental issue with the temperature jumps at certain points in the domain (it is likely that these points are at the interface boundary and I need to verify this). I tried checking the time steps, CFL conditions and other controls but there appears to be no issue with that

3)    Further, a crystallization or melting problem in the code solves in order :

a)    Stefan’s law,

b)    Gibbs Thomson equation,

c)    Level – set equation

d)    Level – Set re-initialization

e)    Diffusion (Energy Equation)

            This also used the framework of the cut – cell method

            Now, there is something peculiar with the code. Let us say we are in the very 1^st loop of the code run. In the event ‘init’, when I check the values of temperature at the end , they are all in bounds. However, the moment we enter event velocity (without any line being executed in between the previous event end and this event start), if we output temperature, we see temperature going out of bounds at interface cells.

4)    Further, If I slightly change the boundary conditions by changing the supercooled liquid temperature , for example, the liquid temperature (TL) altogether fails to converge. Now, since we are solving level -set equation using time marching as we use for hyperbolic equations and I have checked the time step, which appears to be right, the problem could likely be in Diffusion equation.

5)    Now, for solving the diffusion equation ,we use matrix inversion, the way it is used to solve elliptical equations. There appears to be some problem here. 

6)    I also observe the same problem with melting case, where wither the boundary temperature goes out of bunds or I get a message, which shows liquid temperature “TL” failed to converge after some time.

7)    It is also the case that in some simulation runs, if I reduce the time step size, I no longer het the ‘TL convergence failed’ message and the simulation completes the entire run but despite that, the temperature jump at certain cells in the domain is still observed.

There are three cases in particular, I am simulating.

There is a server error on Basilisk now but I will be uploading the following three cases in my sandbox named ‘kaustubh’ as soon as possible, where I have also inserted the print statements to regularly check temperature outputs in files.

The names of these cases in my sandbox are:

1)    Cube sixfold – 2 Dimensional crystallization case

2)    Cube_3d – 3 Dimensional crystallization

3)    Melting_crystal – Melting case

I would be very grateful for any guidance / information regarding this issue.

Please find attached an interesting result, that I have obtained by simulating my cases

  

Thanks & Regards

Kaustubh