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The phase-field method in the sharp-interface limit: A comparison between model potentials. (English) Zbl 0868.65094

The phase-field (PF) method is briefly discussed. Two common choices for the PF potential, here referred to briefly as the Caginalp and Kobayashi models, are compared with respect to their numerical results within the classical sharp-interface limit. Both qualitative and quantitative behavior are addressed, and an assessment of the computational effort required to approximate a sharp-interface problem is made. It is shown that the specific form of the free-energy potential does have a strong influence on the convergence of the PF results to their sharp-interface limit.
Compliance of the PF solutions with the linear kinetic model for the interface temperature is also investigated. A simple one-dimensional solidification problem in the presence of kinetic undercooling is solved by the PF model and also by a deforming grid method. The presented numerical simulations provide further indication that the PF method allows for a reliable investigation of complex microscopic solidification phenomena with moderate computational effort.

MSC:

65Z05 Applications to the sciences
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q72 Other PDE from mechanics (MSC2000)
35K05 Heat equation
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
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