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How to simulate the water boiling by Level-Set method

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There is a good example simulating water boiling by phase field.
I am trying to use the Level-Set method. However, I was frustrated by many times of failure.

My problem is how to deal with the interface using weak form contribution.
Level set and Phase field can deal with the multi-phase flow well.
But, if the phase change at the interface happens, weak form equations have to be used to.

In the Phase field example,
the weak form contribution is test(psi)*phi_source+test(p)*usource.
1) I want to know why used test(psi) and test(p) as the test function?
I used test(phips) and test(u) respectively, the results change a lot. But I don't know why. I might know how to get the weak form from strong form, but I don't know how and why to choose the exact test function.

2) I derived the level set form, and tried to add correct weak form to simulate the boiling phase change.
But the results were totally wrong, So, can somebody help me find the way to understand the level set weak form or give me some examples.

Thank you!

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