Numerical analysis with the phase field equations for the Stefan problems

2014/07/24 by Jun-ichi Koga, Koga, Jun-ichi
Materials Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Magnetic Properties and Applications #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Solidification and crystal growth phenomena #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1407.6464

openalex publication_date 2014/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter φ to track the interface on which complicated movements or changes are needed. More precisely, we analyze the dissolution and/or precipitation without the unknown velocity functions like the Navier-Stokes equations numerically.

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