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What is the most commonly used treatment method of the moving interface in the classical two phase Stefan problems with the finite element method. Here I mean the water-ice two phase problem under freeze-thaw cycles. Can anyone give a somewhat detailed explanation?

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there is a very large literature, you could start for example from a textbook; an overview of numerical methods is given here:

In this paper, we present a critical comparison of the suitability of several numerical methods, level set, moving grid and phase field model, to address two well-known Stefan problems in phase transformation studies: melting of a pure phase and diffusional solid-state phase transformations in a binary system. Similarity solutions are applied to verify the numerical results.

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  • $\begingroup$ Thanks for your suggestion of the literature, seems that I have work to do now. $\endgroup$
    – user123
    Commented Nov 2, 2015 at 2:45

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