A numerical analysis of an anisotropic phase-field model for binary-fluid mixtures in the presence of magnetic-field

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Belmiloudi , Aziz ; Rasheed , Amer (2015)
  • Publisher: HAL CCSD
  • Subject: binary alloys | uid ow | anisotropic phase-field | dendritic so- lidification | [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA] | Mixed finite elements | magnetic-field. | stability and error analysis

In this paper we propose a numerical scheme and perform its numerical analysis devoted to an anisotropic phase-field model with convection under the influence of magnetic field for the isother-mal solidification of binary mixtures in two-dimensional geometry. Precisely, the numerical stability and error analysis of this approximation scheme which is based on mixed finite-element method are performed. The particular application of a nickelcopper (NiCu) binary alloy, with real physical parameters , is considered. The study substantiates a good agreement between the numerical and theoretical results, and demonstrates the efficiency of the presented method.
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