A comparison of numerical models for one-dimensional Stefan problems. (English) Zbl 1092.65072
Summary: 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. The comparison shows that the type of phase transformation considered determines the convenience of the numerical techniques. Finally, it is shown both numerically and analytically that the solid-solid phase transformation is a limiting case of the solid-liquid transformation.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 35R35 | Free boundary problems for PDEs |
| 80A22 | Stefan problems, phase changes, etc. |
Keywords:
Stefan problem; phase transformations; similarity solutions; moving grid method; level set method; phase field method; numerical resultsReferences:
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